A Network Theory of Military Alliances
Yuke Li
∗
†
April 12, 2014
Abstract
This paper introduces network game theory into the study of international relations and
specifically, military alliances. Using concepts from graph theory, I formally define defensive
alliance, offensive alliance and powerful alliance, and on the basis of which, develop a novel
network game that takes these forms of alliances as steady states any given collectivity of
countries might evolve into. For the complex variations of the game, I propose a solution
algorithm and show the robustness of the model in affirming many historic facts including
those from World War I and World War II.
1
Introduction
In political economy, scholars have reached the consensus on the lack of an accepted,
theoretically compelling and operational definition of military alliance, the lack of which has
limited the theorizing about alliance behavior. This paper makes a step towards providing
an operational definition (or theory) of military alliances, by addressing a set of critical
questions: How are alliances different? How can alliances help their members and thereby
impact the broader cooperation and conflict between members and outsiders?
The current literature on military alliances has proposed three main theories of alliance
behavior: balance of power, balance of threat and balance of interest. The gist of the bal∗
PRELIMINARY AND INCOMPLETE DRAFT. I am grateful to John Roemer for continuous support and
guidance. I also thank Weiyi Wu for suggestions and help. All errors remain my responsibility.
†
Yuke Li is a Ph.D student at Yale Political Science Department.
1
1 INTRODUCTION
ance of power theory is the specific idea that if one state gains excessive power, the power
might be transformed into offensive capabilities to attack weaker neighbors, which provides
an incentive for the threatened to unite for survival (Waltz, 1979). Instead, Walt argues that
when confronted by a significant external threat, states may choose between the strategies of
balancing and bandwagoning and develops balance of power theory into balance of threats
theory. (Walt, 1987) While balancing is alignment against the prevailing threat, bandwagoning is alignment with the source of danger. States choose to bandwagon because it may be a
form of appeasement. Along similar lines, past scholarship notes many other tactics states can
choose when facing threats, such as buck-passing, chain-ganging, tethering or hedging, and
so forth (Snyder, 1990; Mearsheimer, 2001; Weitsman, 2004; Pape, 2005). However, a criticism can be made that without a carefully developed and commonly understood foundation,
it could be hard to distinguish and mediate different claims because any one of them only
speaks to one facet of reality. Regarding this, Schweller distinguishes between bandwagoning
and balancing on the basis of the respective motivation. (Schweller, 1994) The distribution
of capabilities, by itself, does not determine the stability of the system; an equally important
factor is the interests of countries to which those capabilities are applied, which entails the
basic analysis of costs and benefits. An example is that a hegemony can coexist in harmony
with multiple other great powers because their well-beings are inextricably linked together.
(Schweller, 2010) He thus proposes a balance of interest theory to address the concerns for the
previous two theories: while bandwagoning is commonly done in the expectation of making
gains, balancing is done for security and always entails costs.
Empirically, many investigations on alliances often make use of certain datasets, which
have facilitated the analysis of alliance behavior but whose coding is usually based on the
specific pacts the countries signed, such as the pacts of defense, neutrality, nonaggression and
entente.(Small and Singer, 1969; Gibler and Sarkees, 2004) This typology is straightforward
and useful; however, it adds to rather than reduces the complexity in defining alliances.
First, by applying a de jure definition of alliances, many alliances remain under-defined. For
example, the Triple Alliance in World War I, which had signed defense pacts and would never
have signed “offense” pacts in the first place, still had offensive motives and should have been
2
1 INTRODUCTION
counted as an offensive alliance. So simply using the datasets leaves an intractable issue in
the literature, offense-defense indistinguishability, unaddressed; second, each of the pacts
provides for a certain behavior in the case of a conflict but the kind of behavior provided
for is very different in each case, which creates problems for theoretical purposes. To address
the problems above, a microfoundation is of fundamental importance, showing the need for a
rigorous and repeatable methodology. (Dolan, 2007) Strategic-interaction models or any kind
of formalism would be useful for this purpose. Previous models in the literature, for instance,
Smith’s two-stage games in alliance formation (Smith, 1995) and Morrow’s model of arms
trade-off (Morrow, 1991), can work in many scenarios but network game can be a much
more ideal alternative. From an empirical perspective, alliances are essentially networks and
the structural characteristics do influence the strategies of both signatories and outsiders;
second, from a theoretical perspective, modeling agents’ “network behavior” can incorporate
many forms of extra-dyadic relationships, which can broaden the analysis to a good extent.
Figure 1: a and b are allies and b and c are foes
Consider the collection of countries with different interests and power in Figure 1 above.
To represent interests, we may assume country a and b are allies and country b and c are
having a war. We go on to assume each has some material power. We then examine how
countries optimally allocate resources to their different interests or relations. For example,
country a has to decide on the proportion of its total resources to spend on supporting b’s war
with c; country b and c decide respectively on the amount of resources to spend on the war
with each other. Though the basic formulation takes the relations as exogenous and leaves
out “network formation”, understanding countries’ resource allocation to different interests
or “network behavior” in a given relational structure is already a fruitful attempt.
So in this paper, I construct a theory of military alliances using network analysis that
3
1 INTRODUCTION
has integrated systemic features, the alliance structure as well as state characteristics in one
single framework. In particular, I take alliances’ structures as they already are in reality
and explain countries’ resource allocation on networks. The basic idea of the theory is that
aggregating individual countries’ micro-level optimizing behavior gives different macro-level
military alliances.
First, I formally define multiple types of alliances using a combination of graph theoretic
concepts and a resource-allocation framework, which provides basic and essential theorizing
of alliances. The formulation helps to mediate among the three aforementioned existing
theories of alliance behavior, and to pave the way for a network game that eventually produces
these defined alliances as equilibrium. Though still underexploited, network games suit the
analysis of military alliances especially well.
Second, I construct a network game as well as an algorithm that solves any variation of
the game. With the relations (ally, foe or no relation) for any given dyad as given, countries
in the network allocate their total capacity into self-defense, support for allies and threat
towards foes. The allocation should be optimal for these countries such that they obtain
the highest possible utility associated with the state attained. Here I define an Alliance
Network Nash Equilibrium as the solution concept, meaning that given the strategies of
all the other countries, any country would have no incentives to deviate from the current
strategy. Aggregating the optimizing behavior of countries give different forms of alliances
as steady states, such as defensive alliance and powerful alliance.
The model is related to the current scholarship on networks and specifically on network games. (Bala and Goyal, 2000; Jackson and Wolinsky, 1996; Konrad and Kovenock,
2009; Bloch and Jackson, 2006; Hiller, 2011; Jackson and Zenou, 2012; Papadimitriou, 2003;
Menache and Ozdaglar, 2011) It even furthers the current studies by embedding a resource
allocation framework into graphs. The model also borrows insights into modeling alliance behavior from some statistical analyses of political networks in political science literature. For
instance, Warren has shown stochastic actor-oriented models combined with Markov simulations of network evolution to be a productive alternative method of modeling interstate
alliances, which allows the incorporation of extra-dyadic interdependence; Maoz’s analysis of
4
1 INTRODUCTION
alliance and trade networks over the 18702003 period reveals strong evidence that alliance
networks are affected by the “homophily” processes.(Maoz, 2012)
Third and lastly, I test the model with two conflicts involving the most complex alliance
dynamics we ever know of – World War I and World War II. The empirical testing consists
of two parts. First, I draw up the network structures of the two wars in consecutive years
and solve each game with the algorithm, using real data on states’ military expenditure
and relation patterns. I then match the game solution with historic facts. Second, I conduct
simulations which predict the likelihood for any country in the given game to be in any state
(aggregating the probabilities for individual countries, I derive the probabilities for different
alliances to occur as equilibrium). The network games in World War I and World War II
yield empirical regularities that are consistent with historic facts. Notably, the model and
the algorithm work even better with interstate conflicts of more complex relation patterns.
In all, this paper makes two main contributions: first, it imports and adapts concepts in
graph theory into use for political economy, providing an operational concept (or theory) of
military alliances. It also has laid a solid micro-foundation for military alliances with a novel
network game; third, the model is highly useful for corroborating many historic facts. I have
tested the game and the solution algorithm with examples from World War I and World War
II.
1
To my knowledge, this paper is the first attempt to operationalize military alliances. It
is also the first one in international relations to use network games for theory building and
for a systematic testing of the two great wars.
The paper is organized as follows: I propose a formal definition of alliances as well as a
theoretical mechanism to explain how alliances are different from each other. On this basis, I
work through the game that predicts alliance behavior and alliance patterns in equilibrium.
Lastly, I present results from empirical testing.
1
Games for smaller-scaled conflicts involving military alliances are simple and can be solved without running
the optimization algorithm.
5
2 A NETWORK GAME OF ALLIANCES
2
A Network Game of Alliances
The new definition of military alliances is adapted from a graph-theoretic definition. This
graph-theoretic definition builds on a political logic: an alliance is a collection of entities such
that the union is stronger than the individual, which can either function to protect against
attack, or to assert collective will against others. This definition was first articulated by Kristiansen, Hedetniemi and Hedetniemi.(Kristiansen, Hedetniemi and Hedetniemi, 2004) They
argue that in graphs any given collectivity of nodes is an alliance and the node connectivity
determines its type — defensive, offensive or powerful. Informally, given a graph G = (V ; E),
a set V is an offensive alliance if every other vertex that is adjacent to V is outgunned by V .
In recent years, researchers in graph theory and theoretical computer science have furthered
the studies of alliances in graphs along similar lines(Bermudo et al., 2010; Brigham, Dutton
and Hedetniemi, 2007; Dutton, 2009; Rodrı́guez-Velazquez and Sigarreta, 2006; Sigarreta,
Bermudo and Fernau, 2009) .
Formally speaking, the original definition of alliances assumes all the edges are of equal
weight and models the number of all connecting nodes as the overall defense support. However, for this specific application, I refine it further to incorporate the resource-allocation
structure: the nodes are countries; the node connectivity denotes bilateral relations (or state
interests), such as between allies or foes; the edge weights denote state investments on those
relations. So for instance, the defense support for a given country should be modeled by the
sum of its connected edges’ weights rather than the number of its connected nodes.
With this refinement, the graphic-theoretic definition of alliances becomes political-economic
— alliances can be defined on the basis of the type and amount of the capability investment.
Alliances are defensive if their defensive capabilities are sufficient to ward off any attacks
towards them. Alliances are offensive if their foes are vulnerable. This can be due to the
offensive capabilities of the alliances that are sufficient to crush the defense of their foes. If
an alliance is both offensive and defensive, it is powerful. From the perspective of a network
game, they can be viewed as equilibria or steady states a given collectivity of states converges
to.
6
2.1
The Network Mechanics
2.1
2 A NETWORK GAME OF ALLIANCES
The Network Mechanics
Consider a directed graph G = (V, E), where V denotes the set of all countries and E
denotes the set of relations between countries.
Definition 1. Node A node in the graph represent a country. I assume that one country
can support another country, attack it or do nothing. These three actions represent three
types of relation: “ally”, “foe” and “none”.
Definition 2. Connectivity Directed edges between nodes represents the relation they
have. Any two connected nodes are either “allies” or “foes”. A and Φ are two disjoint sets of
E that A ∪ Φ = E. A refers to the collection of all ally relations. If (i, j) ∈ A, i will support
j in this game. Similarly, Φ refers the collections of all foe relations.
If two countries have no relations, they can not affect each other’s strategy, so they are
not connected. So if country i has no relations with country j, (i, j) will not be in the set E.
Definition 3. Succeeding Node and Preceding Node In (i, j), j is i’s succeeding
node, which means country i initiates certain behavior towards j. In other words, i is j’s
preceding node. Succ(i) = {j|(i, j) ∈ E} denotes i’s all succeeding nodes, and P red(i) =
{j|(i, j) ∈ E} denotes i’s all preceding nodes.
Specifically, Succ(i) can be a country i attacks or defends; similarly, P red(i) can be a
country attacking i or defending i. A more convenient notion N (i) = P red(i) ∪ i represents
∪
the closed in-neighborhood2 of i. ∂V = i∈V Succ(i) \ V represents the out-neighborhood of
V.
Definition 4. Node Capacity ci is the capacity of country i, which denotes the overall
national capabilities. C is the collection of countries’ national capabilities.
Definition 5. Edge Weight wi,j is the weight of i’s relation to j. wi,j denotes the amount
∑
of capabilities i invests towards j. If (i, j) ∈
/ E, wi,j = 0 and (i,j)∈E wi,j + wi,i ≤ ci .
2
“Closed” means N (i) contains i itself.
7
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
If (i, j) ∈ A, wi,j measures the defense support i gives to j; if (i, j) ∈ Φ, wi,j measures
the offense u have for j. wi,i is i’s self-defense. The total efforts i invests for self defense,
support for its allies and threat for its foes must not exceed its total capacity.
Before proceeding to the game, some specific definitions should be made. By assumption,
any node i (or country i) in the graph is either ally or foe with its connected nodes. It can
be further defined as below that there are four sets of relations between i and its connected
nodes.
Definition 6. Ally Set and Foe Set Ai and Φi are two disjoint sets of Succ(i). Ai =
{j|(i, j) ∈ A} refers to the set such that country i defends as allies and is therefore called
the ally set of i. Similarly, Φi = {j|(i, j) ∈ Φ} will be i’s foe set, the set of countries that
i threatens.
Definition 7. Support Set and Threat Set Ξi and Θi are two disjoint sets of P red(i).
Ξi refers to the set that defends country i as allies and is therefore called the support set
for i. Similarly, Θi will be i’s threat set, the collection of countries that threaten i.
On the basis of the four sets, a behavioral assumption can be made that for any country
in an alliance, it has to support its allies and be supported by them3 ; additionally, for
any country with foes, it threatens them and is threatened by them. We can formally
denote the total support and threat facing any country.
∑
Definition 8. Total Support and Total Threat ξi = j∈Ξi wj,i + wi,i represents total
∑
support for country i; and θi = j∈Θi max{wj,i − wi,j , 0} represents total threat for country
u.
4
2.2
The Game
On the basis of the network mechanics, consider the following game: I model a multiplayer
game with complete information, which incorporates the decision structure of each country
3
A country under the other’s protection is not considered as ally, because it solely receives support.
Note that with the assumption of directed graph, mostly we have that wj,i ̸= wi,j if the links between i and
j are bidirectional, which means the mutual defense contributions in an alliance are not equal.
4
8
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
as investing the total capacity towards self-defense, support for allies and threats towards
foes. Formally, the game is specified by the collection Γ = {V, R, R, Λ, C, C, W, s, u}.
The mathematical representation of the game is as follows:
• A collection of countries V = {1, 2, . . . , N }.
• A collection of relations R = {self, ally, foe, neutral} and a matrix R = [ri,j ] ∈
RN ×N assigning relations between countries. We require that ∀i ∈ V, ri,i = self;
∀i, j ∈ V , if ri,j = ally or foe, then rj,i = ally or foe.
• A matrix Λ = [λi,j ] ∈ (0, 1]N ×N assigning willingness of investment to countries.
Country i’s willingness of investment for j is λi,j . It is the ratio that denotes the
maximum support i is willing to give to j relative to i’s total capacity.
• A compact set of possible capacities C ⊂ R+ and a vector C = [c1 , . . . , cN ]T ∈ C N
assigning ci to country i as its capacity.
• A compact set of strategy C N for each country. Denote strategy of country i as Wi =
[wi,1 , . . . , wi,N ] ∈ C N where wi,j is the investment of country i to country j. The adT T
] describes the investment distribution. We require
jacent matrix W = [W1T , . . . , WN
that ∀i, j ∈ V, wi,j ≤ λi,j ci , and ∥Wi ∥1 = ci .
• A state function σ : C N × RN → [0, 1]N assigning N pairwise states to any country
based on its interactions with the other countries.
• A utility function or characteristic function u : [0, 1]N → R assigns the final state to a
country based on its pairwise states.
Some basic concepts can now be formalized as follows:
• E = {(i, j)|i, j ∈ V, ri,j ∈ {ally, foe}}
• A = {(i, j)|i, j ∈ V, ri,j = ally}
• Φ = {(i, j)|i, j ∈ V, ri,j = foe}
A
S
Three auxiliary relation matrices RA = [ri,j
] ∈ {0, 1}N ×N , RS = [ri,j
] ∈ {0, 1}N ×N and
9
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
Φ
RΦ = [ri,j
] ∈ {0, 1}N ×N are defined as
A
ri,j
S
ri,j
Φ
ri,j

 1
=
 0
ri,j = ally
(1)
otherwise

 1 ri,j = self
=
 0 otherwise
(2)

 1 ri,j = foe
=
 0 otherwise
(3)
RA is the adjacent matrix of A, and RΦ is the adjacent matrix of Φ. RS is an identity
matrix.
Assumption 1. Complete Information Each country in the game knows all the total
capacities and all the relations for those involved. Formally, relation function r, willingness
function ι, capacity function c, state function σ, and utility function u are known to everyone
in the game.
Assumption 2. Allocation of Investment Each country allocates the total capacity into
the usages of self-defense, support for allies (if there are any) and threat towards foes (if
there are any).
Formal definitions of the state and the utility can be represented as below.
Definition 9. State The state matrix S = [si,j ] ∈ [0, 1]N ×N denotes pairwise states.
si,j describes the effectiveness of the influence i exerts on j. Si = [si,1 , . . . , si,N ], S′i =
[s1,i , . . . , sN,i ]T .
Definition 10. State Function Country i calculates its states using a state function σ, a
function of Wi′ = [w1,i , . . . , wN,i ]T and R′i = [r1,i , . . . , rN,i ]T . S′i = σ(Wi′ , Wi , R′i ). Specif′
′
′
S
S T
A
A T
Φ
Φ T
ically, RS i = [r1,i
, . . . , rN,i
] , RA i = [r1,i
, . . . , rN,i
] and RΦ i = [r1,i
, . . . , rN,i
] . The state
10
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
function is identical in form for each country. Formally, we have,
S′i = σ(Wi′ , Wi , R′i )
′
= min{1,
′
′
Wi′ · (RA i + RS i )
max{0, Wi′ − WiT } · RΦ i
′
A′
}R
+
min{1,
}RΦ i
i
′
′
′
′
T
′
Φ
A
S
max{0, Wi − Wi } · R i
Wi · (R i + R i )
′
(4)
′
′
In this equation, (Wi′ · (RA i + RS i )) is actually ξi , and (max{0, Wi′ − WiT } · RΦ i ) is θi . For
′
′
W′ ·(RA +RS )
i
i
i
instance, if rj,i = ally, sj,i = min{1, max{0,W
′ −WT }·RΦ ′ }. sj,i is capped to be 1 if ξi > θi .
i
i
i
However, for rj,i = foe, sj,i is 1 if ξi < θi . After obtaining S′i for N countries, S and Si can
be automatically derived.
Definition 11. Utility Function Country i calculates its utility using utility function u
with Si = [si,1 , . . . , si,N ] and Ri = [ri,1 , . . . , ri,N ]. Ui = u(Si , Ri ). The utility function for
each country is identical. It takes a complex form and as will soon be discussed, is piecewise
continuous.
Formally, we have


Si · RSi



Ui = u(Si , Ri ) =




Si · RSi < 1
1 + Si · RA
i
A
Si · RSi = 1 and Si · RA
i < ∥R ∥1
1 + ∥RA ∥1 + Si · RΦ
i
otherwise
(5)
For simplicity, the utility function is a complete characterization of four situations or realistic
states any country could be in:
1. vulnerable country i’s support does not add up to its threats. In other words, si,i =
Si · RSi < 1;
2. self-defensive country i’s support exceeds its threats, but the support for at least
∑
one of its allies does not exceed the threat. In other words, j∈Ai si,j = Si · RA
i <
∥RA
i ∥1 = |Ai |;
3. defensive for country i and all its allies’, the support exceeds threats, but at least one
∑
Φ
of i’s foes is not vulnerable. In other words, j∈Φi si,j = Si · RΦ
i < ∥Ri ∥1 = |Φi |;
4. powerful for country i and all its allies’, the support exceeds threats, and all i’s foe
11
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
Φ
are vulnerable. The utility reaches its maximum, 1 + ∥RA
i ∥1 + ∥Ri ∥1 = |Succ(i)| + 1.
The utility function and the four situations only constitute one interpretation of the
state matrix. The state matrix contains much more information that can be used for decision
making. Nevertheless, this special form of utility function conforms to two important realistic
assumptions about countries’ preferences in resource allocation.
Therefore, the maximization problem for each country is:
maximize
Ui (W)
subject to
∀j ∈ V, wi,j ≤ λi,j ci , and ∥Wi ∥1 = ci
Wi
(6)
By making such investments, countries can reach certain utility as specified previously. The
four situations in the utility function are actually ranked by order and thereby operationalizes
a preference structure for countries’ investment.
Assumption 3. Each country weakly prefers investing in self-defense to investing in defense
support for allies.
Assumption 4. Each country weakly prefers investing in defense (self-defense and defense
support allies) to investing in offense.
Given the preferences, when the total support for i, ξi , including its self-defense efforts
and assistance from allies, exceeds the total threat, θi . I assume that the country in question
will invest all the resources in self-defense rather than allocating some to support allies if
there are any. Its state si will be smaller than 1 as previously defined. By the same logic, only
if it has sufficient resources for self-defense, it will invest additional resources on supporting
its allies; and only when it is able to self-defend and defend all allies, it will invest additional
resources on attacking its foes. Trivially, it can be seen that country i’s utility increases with
its total capacity ci .
Obviously the utility Ui is a function of the power distribution and is piecewise continuous
in terms of total capacity ci . For example, suppose a and b are foes of c. ca = 2, cb = 2,
cc = 4. We have that Uc =
4
4
= 1. However, a small increment in cc will make Uc 3 because
12
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
now sc,a + sc,b + 1 = 2 + 1 = 3. So it is piecewise continuous.
If all of country i’s foes are vulnerable (not necessarily because of attacks from i5 ),
we can call i offensive. Since I have assumed countries would prioritize self-defense over
support for allies, and defense over offense. offensive only exists theoretically but it will
not happen as a steady state. The countries, by investing in the three kinds of capacities
— self-defense, support for allies and threat towards foes, try to attain the highest possible
state. For countries with both allies and foes, the highest state it could obtain would be
powerful; for countries with only allies, it would be defensive; for countries without allies,
it would be self-defensive. So the highest possible state for any country to attain would
be powerful.
Assumption 5. In terms of relation intensities, ally and foe both describe continuums of
relations.
Importantly, solving the game needs the realistic assumption on countries’ interest, their
willingness to invest, which is previously captured by ωi,j . This assumption extends the
understanding of allies and foes from two extremes to a spectrum. It measures every country’s
relation intensity with each ally and foe at any point of them.
How much efforts countries are willing to invest towards certain relation is a factor not
much emphasized in the current literature; in addition to countries’ capacities and relations,
“issue salience” is crucial to almost every event. The differences in relation intensities can be
attributed to various factors, such as contiguity/geography (in old time, it would be harder
for a distant country to move its troops overseas to help some allies in conflict), and certain
idiosyncrasies(the allies might need to cope with geopolitical threats or unintended events
with discretionary resources).
T T
Definition 12. Deviation Let country i’s deviation from strategy profile W = [W1T , . . . , WN
]
be ∆i = [δj,k ] ∈ RN ×N that ∀j ̸= i, δj,k = 0 and W̃ = W + ∆i is a valid strategy profile.
Theorem 1. Alliance Network Nash Equilibrium (ANNE)
5
This point will be elaborated in the next section.
13
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
Let Γ = {V, R, R, Λ, C, C, W, s, u}. be a game with N players, where Wi is the strategy
set for player i, and Ui is the payoff for player i. When each player i ∈ V chooses strategy
T T
Wi resulting in strategy profile W = [W1T , . . . , WN
] then player i obtains utility Ui . Note
that the state depends on the strategies chosen by all the players. A strategy profile W∗ is
an Alliance Network Nash Equilibrium if no unilateral deviation in strategy by any single
player is profitable for that player, that is ∀∆i , Ui (W∗ ) ≥ Ui (W∗ + ∆i ).
While a formal proof of equilibrium existence is hard to derive, many examples in which
the equilibrium exists can be given.
Example 1. A Three Player Case There are nine relation structures for a three-player
case of countries a, b and c as below in Figure 2.6 The seven relations are of two categories:
1. the three countries in the first four subfigures represent a connected graph; in other words,
any two of the three has a relation; 2. the latter five subfigures mean two of the three have
no bilateral relation.
Take the first graph as example. Assuming the willingness parameter to be 100%, the
equilibrium still requires a discussion of the power distribution. Then there are three cases
to consider:
Case 1: ca + cb > cc . First, it is definite that a and b are self − defensive and c is
vulnerable. Given that a and b are allies, a and b are defensive.
With the assumption on countries’ priority in defense, c will not use most or all resources
on defeating one foe even if it might be able to. Rather, it will use all the resources for
defense against a and b because in this case its threats are larger than the support.
Furthermore, if at least one of a and b has more individual capacity than that of c, the
country (countries) will be powerful; otherwise, both of them will be defensive and c is still
vulnerable.
In any of the possibilities, none of them has incentives to deviate.
Case 2: ca + cb = cc . This case only has a type of equilibrium where each country is
defensive. Further, a and b are defensive and c is self − defensive.
6
Note that here I exclude the cases of unilateral relations and the case where the three have no relation with
any other.
14
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
c
a
b
15
Figure 2: Red lines mean “foe” and green lines mean “ally”
2.2
The Game
(a) c(a) + c(b) > c(c)
2 A NETWORK GAME OF ALLIANCES
(b) c(a) + c(b) = c(c)
(c) c(a) + c(b) < c(c)
Case 3: ca + cb < cc . First, a and b are vulnerable. It is obvious that c is powerful.
None of them has incentives to deviate. □
I can proceed to derive the equilibrium similarly for the rest of the relation structures.
The first to notice is that holding the relations constant, the situation or state each would
possibly be in is a function of their power and the willingness to invest in any type of
relation; and holding their power and interest constant, their states in equilibrium turns into
a function of their relations, i.e. node connectivity. Furthermore, comparing to a and b having
a mutual enemy c in the first figure, b’s two allies, a and c, are foes in the second figure.
Such distinction would be explored further in the definition of complete alliance in the next
section, where I will show how this distinction can make different alliances in equilibrium.
Example 2. Multiple States Consider the example: a and b are allies and both of them
are in conflict with c. Assuming the total capacities ca = 30, cb = 10 and cc = 20. Figure
4 illustrates an equilibrium in which each country represents a different state and has no
incentives to deviate to other states given the state of the others: a is powerful (it invests 21
in offense towards c and keeps 9 as self-defense), b is defensive (its ally a and itself are both
self-defensive) and c is vulnerable.
7
Example 3. Multiple Types of Equilibria Consider the following example that illustrates the case of multiple equilibria: c is in conflict with a and b respectively. We assume
7
Red pointed edges represent relation foe and green pointed edges represent relation ally. Investments on the
red pointed edges denote threat towards the foes and investments on the green pointed edges denote support for
allies. For simplicity, ι = 1 for all relations in the examples of Section 2.
16
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
Figure 4: Multiple States
Sa = powerful, Sb = defensive and Sc = vulnerable
ca = 5, cb = 9 and cc = 5. There will be two equilibria illustrated in Figure 5 and 6: the
first with a, b and c all being defensive, and the second with a and c being powerful and b
vulnerable.
For the first case, with c’s strategies staying fixed, however a changes its investment will
not change its state. b does not have enough capacity to overwhelm a and c and cannot
promote itself to a higher state, either. In the second case, a and c have reached their highest
possible state, while b on the other hand does not have enough capacity to be self-defensive.
Figure 5: Type 1 Equilibrium
Sa = defensive, Sb = defensive and Sc = defensive
Figure 6: Type 2 Equilibrium
Sa = powerful, Sb = vulnerable and Sc = powerful
17
2.2
The Game
2.2.1
2 A NETWORK GAME OF ALLIANCES
Equilibrium Analysis: A Characterization of Different Alliances
Aggregating all the countries’ maximizing behavior produces the aforementioned equilibrium. Different types of alliances in equilibrium can be the end products to which collectivities
of countries converge, which can be defined formally as below.
8
Definition 13. Alliance. For a set of countries V , ∀i, j ∈ V , r(i, j) ̸= foe and ∀i ∈ V ,
∃j ∈ V s.t. r(i, j) = ally or r(j, i) = ally.
Definition 14. Complete Alliance. An alliance V is complete if ∀i ∈ V and ∀j ∈
/ V,
r(i, j) ̸= ally.
Using a concept of defensiveness, I define types of alliances to represent some possible
end products of countries’ behavior.
Definition 15. Defensive Alliance. An alliance V is a defensive alliance against a set of
∑
countries Z if all countries in V are self-defensive against Z, ∀i ∈ V, ξi ≥ j∈Z∩Θi max{0, wj,i −
wi,j }.
ξi represents all the defense capabilities any country i in alliance can have, which include its own defensive investment and allies’ support, even from allies in other alliances.
∑
j∈Z∩Θi wj,i represents the the threats facing i. So long as all countries’ defense capabilities exceed enemies’ offense efforts, they can ward off threats and form a defensive alliance
against the foes. Consider the example in Figure 7, a and b form an alliance, and a and d, d
and c are in conflicts. ca = 2, cb = 0.5, cc = 5 and cd = 4. We can see the alliance formed by
a and b is defensive.
Note that an alliance can be defensive only because of certain strong outsiders who have
mutual enemies with it. In other words, if not for the outsiders’ offense, some alliances could
not have been defensive. Though the alliance in Figure 7 would not have been defensive if the
outsider c had not helped to overcome the threats, it became defensive without the defense
support of c. Accordingly, we have the definition of strictly defensive alliance to allow for
8
A country can be part of several different alliances. Although we do not require mutual support in an alliance,
we do require there is no conflict in an alliance; in other words, there’s no “foe edge” in the graph of an alliance.
18
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
Figure 7: Defensive Alliance
a and b form a defensive alliances
the case that an alliance is defensive only because of the capacities and support among its
member countries. By this definition, the alliance in Figure 7 is both defensive and strictly
defensive.
Definition 16. Strictly Defensive Alliance. An alliance V is a strictly defensive alliance
against a set of countries Z if all countries in V are self-defensive against Z, ∀i ∈ V and
∑
∑
∀j ∈ V , j∈V ∩Ξi wj,i + wi,i ≥ j∈Z∩Θi max{0, wj,i − wi,j }.
Figure 8 shows a strictly defensive alliance formed by a and b, where ca = 5, cb = 5,
cc = 6, because both a and b are self-defensive.
Figure 8: Strictly Defensive Alliance
a and b form a defensive alliance
Proposition 1. If an alliance is complete, defensive alliance is equivalent to strictly defensive
alliance.
Proof: If an alliance is complete and defensive, each country in the alliance does not have
outsider allies and is self-defensive against the set of foes the alliance might have.
By the definition of strictly defensive alliance, we know it must be strictly defensive.
The two concepts are equivalent for a complete alliance. □
We can have both a weak and a strong version of defensive alliance.
19
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
Definition 17. Weakly Defensive Alliance. V is a defensive alliance against country j
if all countries in V are self-defensive against {j}, ∀i ∈ V, ξi ≥ max{0, wj,i − wi,j }.
A weakly defensive alliance can also be called regional defensive alliance because it can
still defend itself in a regional conflict against a single country. Figure 9 shows a weakly
defensive alliance formed by a and b, where ca = 6, cb = 4, cc = 12, cd = 6. Though a is
self-defensive against d, b is vulnerable and a cannot help b to overcome c. So a and b are
only self-defensive against one foe, d.
Figure 9: Weakly Defensive Alliance
a and b form a weakly defensive alliance against d
Definition 18. Strongly Defensive Alliance. V is a strongly defensive alliance if all
countries in V are self-defensive, ∀i ∈ V, ξi ≥ θi .
A strongly defensive alliance can also be called global defensive alliance because even if
every country outside the alliance becomes a foe, the alliance can still defend itself. Figure
10 shows a strongly defensive alliance formed by a and b, where ca = 5, cb = 6, cc = 1,
cd = 6. Obviously, a and b are self-defensive against both c and d.
Figure 10: Strongly Defensive Alliance
a and b form a weakly defensive alliance against c and d
Proposition 2. Countries in Complete Strongly Defensive Alliance must be defensive.
20
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
Proof: By the definition of complete alliance, every country must only be ally with countries also in the alliance. By the definition of strongly defensive alliance, every country in
the alliance must be self-defensive.
This is equivalent to saying every country as well its allies is self-defensive, which is
exactly the definition of “defensive”. So countries in complete strongly defensive alliance
must be defensive.
Note that in non-complete alliance, some countries can be allies with outsiders, who might
not be self-defensive. So countries in non-complete alliance are not necessarily defensive.
An example is given in Figure 11. We assume ca = 1, cb = 1 and cc = 1; a is ally with
both b and c, and b and c are foes. The alliance formed by a and c is therefore non-complete
because a is also ally with an outsider b. Since b has conflict with c, we say a, b and c cannot
form an alliance by the assumption of “no-conflict” in alliances. The equilibrium shows that
a is not defensive because one of its ally b is made vulnerable by c. □
Figure 11: Non-Complete Strongly Defensive Alliance
Sa ̸= defensive
Definition 19. Offensive Alliance. V is an offensive alliance for Z if no country in Z
being V ’s neighbor is self-defensive, ∀j ∈ ∂V ∩ Z, ξj < θj .
As long as the threat is larger than the support, we say Z is vulnerable, regardless of the
origins of the threats. The threats can be from V itself or from elsewhere. To illustrate the
case that Z is vulnerable because of V , I propose a more strict definition of offensive alliance
21
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
below.
Definition 20. Strictly Offensive Alliance. V is a strictly offensive alliance towards
Z if no country in Z being V ’s neighbor is self-defensive against V , ∀j ∈ ∂V ∩ Z, ξj <
∑
i∈V ∩Θj max{0, wj,i − wi,j }.
Strictly offensive alliance is the opposite of defensive alliance. If V is a defensive alliance
against Z, Z will never be a strictly offensive alliance towards V and vice versa. However, Z
can still be an offensive alliance. However, the other threats V might have to make precautions
for could have prevented V from becoming a defense alliance.
Figure 12 represents an offensive alliance and a strictly offensive alliance. We assume a
and c, a and b, d and e, are allies, while c and b, b and d are foes. In addition, ca = 0.5, cb = 8,
cc = 12, cd = 5 and ce = 5. The solution shows the alliance formed by d and e is offensive
alliance, because even though b is vulnerable, it is vulnerable because of c. The alliance
formed by a and c is strictly offensive alliance because it makes the only foe b vulnerable.
Figure 12: Offensive Alliance and Strictly Offensive Alliance
a and c form a strictly offensive alliance; d and e form an offensive alliance
Proposition 3. Strictly offensive alliance must be offensive alliance.
Proof: By definition, if ∀j ∈ ∂V ∩ Z, ξj <
∑
i∈V ∩Θj
max{0, wj,i − wi,j },
it must be that ∀j ∈ ∂V ∩ Z, ξj < θj .
So strictly offensive alliance must be offensive alliance. □
Note that the definition of offensive alliance refers to alliances attacking a set of countries.
Then we can further refine this concept into a weak and a strong version.
22
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
Definition 21. Weakly Offensive Alliances. V is a weakly offensive alliance towards j
if j is not self-defensive.
Definition 22. Strongly Offensive Alliances. V is a strongly offensive alliance if no
country being V ’s neighbor is self-defensive.
Proposition 4. If an alliance Z is the complement of a complete alliance V , Z = V , and if
V is strongly offensive alliance, V is also strictly offensive.
Proof: By the definition of strongly offensive alliance, no country as V ’s neighbor is selfdefensive. Given that Z = V , no country in Z as V ’s neighbor is self-defensive, which is
exactly the definition of strictly offensive alliance.
So if Z is the complement of V , Z = V , strongly offensive alliance is equivalent to strictly
offensive alliance. □
On the basis of the definitions of defensive and offensive alliances, we come to the definition of powerful alliance, by which we refer to such a kind of alliance both strongly offensive
and strongly defensive for its neighbors.
Proposition 5. Powerful Alliance. If V is strongly offensive in equilibrium, V must be
strongly defensive. We call U a powerful alliance.
Proof: “Strongly offensive” and “strongly defensive” are equilibrium concepts.
Given the priority assumption, we know the countries always prioritize defense over offense. So for strongly offensive alliance in equilibrium, it must have already been strongly
defense.
We call this kind of alliance “powerful” alliance. □
Figure 13 illustrates a powerful alliance. a, b and c are allies with one another while d
has conflict with both a and b. We have that ca = 10, cb = 10, cc = 1 and cd = 9. The only
foe for the alliance formed by a, b and c is vulnerable. The alliance is both strongly offensive
and strongly defensive and thus powerful by definition.
23
2.2
The Game
2 A NETWORK GAME OF ALLIANCES
Figure 13: Powerful Alliance
a, b and c form a powerful alliance
Table 1: Notations
Symbol
V
A
Φ
E
wi,j
W
cj
C
λu,v
Λ
Aj
Φj
Ξj
Θj
ξj
θi
πi,j
Si
Ri
Ui
Expression
A∪Φ
∪
(i,j)∈E {wi,j }
∪
j∈V {cj }
∪
(i,j)∈E {ιi,j }
{i|(j, i) ∈ A}
{i|(j, i) ∈ Φ}
{i|(i, j) ∈ A}
{j|(i,
∑ j) ∈ Φ}
i∈Ξj wi,j + wj,j
max{wj,i − wi,j , 0}
θj
ξj wi,j
Explanation
set of nodes (vertices)
set of “ally” edges
set of “foe” edges
set of edges
edge weight of (i, j)
set of edge weights
node j’s node capacity
set of capacities
node i’s willingness of investment for j
set of willingness parameters
“ally” nodes of node j
“foe” nodes of node j
“support” nodes for node j
“threat” nodes for node j
total support for node j
total threat for node j
Node i’s PDR for node j
Country i’s pairwise state vector
Country i’s relation vector
Country i’s utility
24
3 A SOLUTION ALGORITHM
3
A Solution Algorithm
The model operationalizes a basic idea for alliance behavior: with survivalism as the
utmost motive, countries engage in investment in offense and defense capabilities. Country
relations (node connectivity), capacity distribution (node capacity) and investments (edge
weight) combine to determine the type of the alliance. Given these, network theory is not
only important for a operational definition of military alliances but also for a testable theory
for alliance behavior.
Given the complexity of the alliance structures and the possibility of multiple types of
equilibria of the game, it would be efficient to solve the game by computation with an
optimizing algorithm because some variations of the game can be extremely complex. The
game involves the basic idea of evolution, taking countries as entities of learning and imitation
and letting their behavior evolve into certain equilibrium. Obviously many equilibria exist in
most cases. However, I do not pay much attention to the details of those equilibria as long
as they belong to the same type. Instead I pay attention to their properties and distribution.
Starting from any point in solution space, we can always find an equilibrium using a proper
evolutionary algorithm. The probability for each type of the equilibria to occur depends on
the proportion of initial points that finally converge to the equilibrium. We can randomly
sample the solution space and estimate the distributional property. And a proper evolutionary
algorithm like simulated annealing is used for finding an equilibrium to which an initial point
converges.
We have designed and tested an algorithm to compute the optimal allocation between
edge weights (resources invested on attacking or assisting other countries) and node weights
(resources retained for self-defense) in the network games for any type of alliance structure.
We first simulate networks on the basis of node capacity and the connectivities based on
data of military alliances and national capabilities. The algorithm will work in such a way
that we first generate the initial population of edge weights randomly, and then evaluate the
fitness of the edge weights for attaining certain goal, for example, defensive alliance. Such
process will repeat on until termination when a sufficient fitness is achieved.
25
3 A SOLUTION ALGORITHM
Thus, the flow of decisions is described in detail below:
First, all countries randomly assign weights to their out-edges. The assignment does not
have to be optimal (in fact it should not be optimal), but have to be completely random
because we are randomly sampling solution space.
The node weights and all the edge weights will evolve until an equilibrium is reached.
As mentioned previously, we should consider the previous preference issue for countries in
assigning capacities towards various kinds of investments: first, assuming survivalism is of
utmost importance, countries have to fulfill their self-defense requirements; then they may
also have to support their allies; finally if they have extra capacities, they can invest in
offense. A country is impossible to be powerful if it does not have enough capacity to attack
its foes while maintaining its self-defense and its allies’ defense.
Basically, the criterion is that for each country9 ,
1. it is powerful, or
2. it is defensive and incapable of being powerful, or
3. it is self-defensive and incapable of supporting all its allies, or
4. it is incapable of being self-defensive.
Note that although the algorithm works by dynamic updating of edge weights and node
weights until an equilibrium is obtained, the model itself is static per se. Therefore, to
efficiently execute the algorithm, we use an variable named “Proportional Defense Responsibility” to proxy for countries’ investment update in each round.
t
Definition 23. Country i’s Proportional Defense Responsibility for j is πi,j
=
t
wi,j
ξjt
· θjt
(which denotes at round t the proportion of i’s support for j to j’s overall defense support,
t
multiplied by the sums of threat for node v). And πi,i
is called self-defense requirement and
recognized as a form of PDR.
The idea is that in each round of evolution, all countries firstly calculate the proportional
defense responsibilities (PDRs) for itself and its allies. If, holding fixed the external threats,
9
Given that the alliance always prioritizes defense, it would be realistic to further assume that countries’ aim
would be to first sustain a defensive alliance and second, if possible, a powerful one.
26
3 A SOLUTION ALGORITHM
all countries fulfill their PDRs, they will just become defensive at the end of this round. If any
of them has not fulfilled the PDRs, the updating processes will repeat until an equilibrium
is reached. It is possible that they would all be defensive or some of them fail to be even
self-defensive at the end of the updating process.
Formally, for all countries, an updating process will repeat until an equilibrium is reached:
1. Collecting Total Defense Investments
Country v “collects” its defense investments in the previous round including defense
support for allies and its own self-defense, so that they can be reallocated in the new
round.
t−1
κ = wj,j
+
∑
t−1
wj,i
(7)
i∈Aj
κ is the total amount of capacity the country can reallocate on defense.
2. Prioritizing Defense to Offense
Given that the PDRs for v is obviously,
t
P DRjt = πj,j
+
∑
t
πj,i
(8)
i∈Aj
If total defense investments κ is smaller than the sum of the PDRs, country j ought
to “retract” some threats made towards foes (if there are any), in other words, some
offense investments, in order to defend. And if total capacity cj (which includes both
the defense and offense investments) is larger than the sum of the PDRs, country j is
also able to retract some of the previously made threats. Note that this behavior is, in
particular, due to the priority-of-defense assumption we made at the beginning.
Let the amount of offense investments retracted be just sufficient to satisfy the requirements of PDRs. The gaps in resources country j has to fill would be given by (Note
that if the total capacity is not even enough for the PDRs, country j should retract all
27
3 A SOLUTION ALGORITHM
the offenses investments):
∑
t
t
πj,j
+ i∈Aj πj,i
−κ
t−1
(
)wj,i
∑
t−1
i∈Φj wj,i
t
if cj ≥ πj,j
+
∑
t
πj,i
(9)
i∈Aj
t
So the offense investment by j towards i, wj,i
, will be updated into:
t
wj,i





=
∑
t
t
πj,j
+ i∈Aj πj,i
−κ
t−1
(1 −
)wj,i
∑
t−1
w
i∈Φj j,i



 0
t
cj ≥ πj,j
+
∑
i∈Aj
t
πj,i
(10)
otherwise
Now adding the retracted offense investment to the total defense investments κ, which
becomes,

t
 πt + ∑
j,j
i∈Aj πj,i
κ=
 ct
j
t
+
ctj ≥ πj,j
∑
i∈Aj
t
πj,i
(11)
otherwise
3. Prioritizing Self-Defense to Defense Support
The priority assumption also states that countries have to fulfill its self-defense requirement first. In the case that the total capacity is not even sufficient for self-defense,
we assume it should retract all the other investments, use all its capacity just for self
defense and end this round, hoping some allies would assist.
t
wj,j

 πt
j,j
=
 ct
j
t
ctj ≥ πj,j
(12)
otherwise
So if the total capacity is sufficient for self-defense, the remaining capacity can be
retained for other purposes such as defense support for allies.
t
ctj = ctj − πj,j
(13)
28
3 A SOLUTION ALGORITHM
4. Supporting Allies
After fulfilling the self-defense requirement, countries would try to meet PDRs for allies
with what remains of cv (the ctv on the left-handside of Equation 7). If the available
capacity is not sufficient, we let it rescale PDRs so that it can afford them and end this
round, hoping its allies can receive additional support from the other sources. So for
ally i of country j,
t
wj,i
=


t


 πj,i
ctj ≥
ctj

t

∑


t πj,i
s∈Aj πj,s
otherwise
∑
s∈Aj
t
πj,s
(14)
Once again, we go on to update the remaining total capacity ctj .
ctj = ctj −
∑
t
πj,s
(15)
s∈Aj
5. Waging Offense
Finally after meeting both self-defense and PDRs, we assume the country can arbitrarily
spend the extra capacity, such as on offense.
Example 4. 1910 Europe Using the algorithm, we examine the case of the Triple Alliance
and its foes in 1910. Figure 14 represents the investments within the alliance and towards a
foe, Turkey. Note that though having been rescaled, their military spendings reflect the real
capacity distribution. Take Germany as an example: 31.7667 is its self-defense effort; and the
“60” within the bracket denotes the level of total capacity; 52.0047:0 denotes the defenseoffense balance: 52.0047 includes its self-defense and the allies’ support
10
; since Germany
did not have foes that year, it would optimally make 0 offense investment. Just as predicted
by the model, with the support from Germany and Austria-Hungary, Italy became powerful
and defeated Turkey with a large advantage. Germany, Austria-Hungary and Romania were
defensive, Italy was powerful and Turkey was vulnerable. (See Figure 14)
10
This graphical presentation of investments will also be used for all solution graphs in the section of empirical
testing.
29
3 A SOLUTION ALGORITHM
Algorithm 1: Finding wj,i and wj,j
Data: V , A, Φ, C
Result: W
1 begin
2
foreach j ∈ V do RandomSeed (j, cj );
3
repeat
4
t ← t + 1;
5
foreach j ∈ V do
/* calculate supports and threats */
∑
t−1
t−1
+ wj,j
;
6
ξjt ← i∈Ξv wi,j
∑
7
θjt ← i∈Θj max{0, wi,j − wj,i }t−1 ;
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
foreach j ∈ V do
foreach i ∈ Aj ∪ {j} do
t ←
πj,i
/* update weights */
/* calculate PDR */
θit t−1
w ;
ξit j,i
∑
t−1
t−1
κ ← wj,j
/* retract support */
+ i∈Aj wj,i
;
foreach i ∈ Aj do
t ← 0;
wj,i
∑
t +
t
if κ < πj,j
i∈Aj πj,i then
foreach i ∈ Φj do ∑
/* retract threat if cannot defend */
t +
t −κ
πj,j
π
i∈Aj j,i
t−1
t ← (1 −
wj,i
)wj,i
;
∑
t−1
w
i∈Φj j,i
∑
t +
t
κ ← πj,j
i∈Aj πj,i ;
t then
if κ < πj,j
t ← κ;
wj,j
/* use all weights for self defense */
else
t ← πt ;
wj,j
/* self defense */
j,j
t
κ ← κ − πj,j ;
∑
t then
if κ < i∈Aj πj,i
foreach i ∈ Aj do /* use all weights for alliance defense */
κ
t
t ← ∑
wj,i
t πj,i ;
s∈Av πj,s
else
foreach i ∈ Aj do
t ← πt ;
wj,i
j,i
∑
t ;
κ ← κ − i∈Aj πj,i
RandomSeed (j, κ);
(cntto , cnttd ) ←CheckSteady (V , W t );
until cntto = 0 and cnttd = 0;
30
/* alliance defense */
4 EMPIRICAL TESTING
ROM
0.250924(3)
23.1444:0
13.4162
GER
31.7667(60)
52.0047:0
1.36702
7.77375
1.20267
0.0506245
ITA
0.409551(30)
12.9414:0
0.179388
9.42664 1.99817
7.04328
3.55542
25.4485
0
TUR
10(10)
10:25.4485
2.09317
16.8728
AUS
0.145142(30)
9.46097:0
Figure 14: 1910 Europe
Green circles are countries that are self-defensive; blue circles are countries
that are both self-defensive and with whom the foes are vulnerable (not necessarily powerful); though not shown in this graph, yellow circles are countries
that are vulnerable. The Triple Alliance was powerful because it was defensive and its foes was vulnerable. This is an equilibrium because no country
will deviate from the current state.11
4
Empirical Testing
The model can in principal work with interstate conflicts involving military alliances of
any context and geographic scale. The previous example of 1910 Europe is an application of
the model to a geographically small-scaled conflict between an alliance, the Triple Alliance,
and a single country, Turkey. While many more similar cases such as the Gulf War and the
Sino-Japanese war could be studied under the current framework and presented, an empirical
testing with World War I and World War II, the two largest conflicts in human history that
embody the most complex alliance dynamics, adds more credibility to the model.
While the network mechanics in the model can comprise any interstate conflict in history,
I acknowledge certain conditions have to be specified for model testing. First, it has to be
an interstate conflict involving military alliances; otherwise, the specified decision structure
for agents would be of little use. Moreover, as will be shown in the below sections, the effectiveness of the model in restoring historic facts increases with the complexity of the network
31
4 EMPIRICAL TESTING
structures or the number of countries involved. I hypothesize that noises or idiosyncratic
factors could more easily impact interstate conflicts that are structurally simpler. On the
contrary, those involving complex alliance dynamics are more likely to reflect the influences
of what are fundamental to the outcomes of wars – material factors like relative power and
country interest. Second, the conflict is preferably contemporary. Otherwise the study would
be greatly limited by data constraints.
The empirical testing consists of two parts: first, I take the military spendings, alliance
structures and conflict occurrences for the countries involved in the given year as data inputs of the game and illustrate graphically one solution obtained with the aforementioned
heuristic; second, given the existence of multiple types of equilibria, I predict the likelihood
for each type of equilibria to occur by simulations.
I mainly make use of datasets from the Correlates of War project, which include the
National Material Capability dataset, the Militarized Interstate Dispute dataset as well as
the Alliance Treaty Obligations and Provisions (ATOP) dataset. 12 Overall, the data indicates
two patterns in the alliance and conflict dynamics: first, there are more militarized conflicts
than wars; second, as more countries engaged in wars, more countries joined alliances with
each other.13
Note that solving the game relies heavily on the willingness parameter14 , which serves
as an upper bound on the resources any country could make use of in pursuing certain
behavior. For the empirical testing, certain criteria are applied to input the parameter: first,
for a dyad with great contiguity, the willingness parameter for both would be high; second, for
dyads that are confirmed to have been important allies or in intensive wars, the willingness
parameter would also be high. For the rest, I use historic cases to enter the parameters.
12
The country-year variable “military spending” in the National Military Capacity dataset is used to proxy the
total capacity of countries in a given year. For 1816-1913, military spending was coded in thousands of current
year British Pounds; and for 1914 onwards, it was in thousands of current year US Dollars.
13
Please refer to Table 2 - 6 to see these patterns.
14
The year-by-year willingness parameters for any country in any given relation will be given in supplementary
materials.
32
4.1
A Visualization of Europe in World War I
4.1
4 EMPIRICAL TESTING
A Visualization of Europe in World War I
I first examine the period from 1914 to 1918 in Europe. In the decade before the start of
the World War I, two alliances gradually formed. One was by Germany in alignment with
Austria-Hungary and Italy, forming what was known as the “Triple Alliance”. The other
started with France cultivating friendship with Russia after the Franco-Prussian war in the
1870s, then with Britain seeking out an alliance with these two continental powers, which
became the “Triple Entente”.
There are four main results from the empirical testing, which are:
Result 1: Germany had faced an increasing probability of failure as the war dragged on.
Result 2: Without the entry of the US, Germany could have been defensive and reversed
the disadvantage because it had accumulated tremendous power in 1918
Result 3: As Russia’s resources were being depleted and even much of it had to be
diverted to deal with the domestic revolution, this greatly impaired the prospect for retaining
a powerful state
Result 4: The entry of the US helped the UK and France greatly. Obviously, these
regularities are consistent with historic facts.
4.1.1
1914-1915
The map in Figure 15 shows the geopolitical situation of Europe as of the year of 1914:
the country dyads in wars, in militarized conflicts (not wars) and in bilateral defense pacts.
The first two sets of relations are denoted by red lines while the third relation is captured
by green lines. More specifically, I listed all the relations below in Table 2.
The relation patterns show that Germany was at war with some major powers such as
the UK, France and Russia. The results of the game show that given the capacity distribution, country relations and their willingness to invest, neither Germany nor Austria-Hungary
was successful in these two years. To empirically account for these results, initially Germany opened the war on the Western Front, which was intended to quickly conquer France
through Belgium. However, Belgium fought back and sabotaged the German rail system,
33
4.1
A Visualization of Europe in World War I
4 EMPIRICAL TESTING
Figure 15: Geopolitics of Europe in 1914
Figure 16: Geopolitics of Europe in 1915
34
4.1
A Visualization of Europe in World War I
4 EMPIRICAL TESTING
Table 2: 1914 Relation
Dyads in War
UK - Germany
UK - Austria-Hungary
UK - Turkey
Belgium - Germany
France - Germany
France - Austria-Hungary
France - Turkey
Germany - Yugoslavia
Germany - Russia
Austria-Hungary - Russia
Austria-Hungary - Yugoslavia
Yugoslavia - Turkey
Russia - Turkey
Dyads in Militarized Conflict
UK - The Netherlands
UK - Norway
The Netherlands - Germany
The Netherlands - Russia
Switzerland - Germany
Switzerland - Austria-Hungary
Portugal - Germany
Germany - Romania
Germany - Sweden
Germany - Norway
Germany - Denmark
Italy - Albania
Yugoslavia - Bulgaria
Austria-Hungary - Italy
Greece - Bulgaria
Greece - Turkey
Romania - Turkey
Dyads in Alliance
UK - Portugal
Germany - Austria-Hungary
Germany - Italy
Austria-Hungary - Italy
Germany - Romania
Romania - Austria-Hungary
Italy - Romania
France - Russia
Yugoslavia - Greece
Bulgaria - Turkey
Austria-Hungary - Bulgaria
Germany - Bulgaria
Russia - Romania
which greatly delayed Germany. Though Germany was very successful in earlier battles in
1914, France with assistance from the British forces halted the German advance at the First
Battle of the Marne. Importantly, German armies intended for the Western front were also
diverted to cope with Russia’s attacks on the Eastern front.(Foley, 2006; Keegan, 1999) Aside
from the cooperation between France and Britain, Germany also suffered from the problems
of communications and questionable command. Additionally, in 1915, Austria-Hungary soon
entered war with Russia, which greatly limited its coordination with Germany.(Keegan, 1999;
Strachan, 2001)
Also, through the relation patterns in 1915, we can see that Italy revoked the Triple
Alliance and joined the Entente against Germany and Austria-Hungary. So despite the quick
victories in the early phases of the war, these unfavorable factors landed Germany in besiege,
making it extremely difficult to be “defensive” or “powerful”, as has been shown in Figure
9 and 10.
35
4.1
A Visualization of Europe in World War I
4 EMPIRICAL TESTING
Table 3: 1915 Relation
Dyads in War
UK - Germany
UK - Austria-Hungary
UK - Turkey
Belgium - Germany
France - Germany
France - Austria-Hungary
France - Turkey
Germany - Yugoslavia
Germany - Russia
Austria-Hungary - Russia
Austria-Hungary - Yugoslavia
Yugoslavia - Turkey
Russia - Turkey
UK - Bulgaria
France - Bulgaria
France - Turkey
Germany - Italy
Italy - Bulgaria
Italy - Turkey
Yugoslavia - Bulgaria
Bulgaria - Russia
Dyads in Militarized Conflict
Bulgaria - Turkey
UK - Sweden
The Netherlands - Germany
The Netherlands - Russia
Belgium - Austria-Hungary
Belgium - Bulgaria
Belgium - Turkey
Germany - Romania
Germany - Sweden
Germany - Norway
Germany - Denmark
Italy - Albania
Italy - Bulgaria
Greece - Turkey
Romania - Turkey
France - Sweden
Spain - Germany
Portugal - Germany
Austria-Hungary - Italy
Austria-Hungary - Sweden
Albania - Yugoslavia
Greece - Bulgaria
Russia - Sweden
36
Dyads in Alliance
UK - Portugal
Germany - Austria-Hungary
Italy - Russia
France - Italy
Germany - Romania
Romania - Austria-Hungary
Italy - Romania
France - Russia
Yugoslavia - Greece
Bulgaria - Turkey
Austria-Hungary - Bulgaria
Germany - Bulgaria
Russia - Romania
UK - France
UK - Italy
UK - Russia
0
58430
00
13948.5
839422
82364.2
0
0
3910.5
0
464116
368707
2627.830
0
0
0
GRC
3519.45(7821)
3519.45:0
20150.1
0
214.45
6.04365
0
4495.5
FRN
48372.6(1.235e+06)
50438:0
6320.65
428500
41.0518
0 43726.5
9038.830552225
03861.44
AUH
673293(1.042e+06)
1.16326e+06:1.21873e+06
1287.664495.5
BUL
0(10483)
429.055:0
599941
5704.43
391.05
429.0551817.77
0
28575.1
248.9
159.522
97.722 0
51125.9
0
0
4803.79
GMY
1.28434e+06(1.785e+06)
1.70309e+06:1.84286e+06
0
0
TUR
45586(45586)
50389.8:120369
335769
0
22991.71598.69
329625
0
501.2
1109
11980.2
0
DEN
4074.55(4289)
4074.55:0
5886.812065.36
2198.44
0
RUM
0(8991)
13267.9:0
5.28961
0
17490.6
0
NOR
8107(8107)
8107:51285.4
RUS
70540.3(857000)
76427.1:0
1109
0
ITA
23608.1(87453)
23649.1:0
5249.840
SWE
19962(22180)
19962:0
BEL
9847(9847)
9847:2198.44
NTH
7849(7849)
7849:25405.2
A Visualization of Europe in World War I
37
Figure 17: 1914 Europe
As previously represented, Green circles are countries that are self-defensive,
blue circles are countries that are both self-defensive and with whom the foes
are vulnerable, and yellow circles are countries that are vulnerable.
YUG
4156(4156)
8066.5:5843
ALB
1663(1663)
1663:2627.83
UKG
327021(1.67884e+06)
328620:0
POR
3130.41(4978)
26122.1:0
SPN
99874(99874)
99874:0
4.1
4 EMPIRICAL TESTING
Figure 18: 1915 Europe
38
0
0
4673.5
0
0
467.35
00
214.45
0
00
0
37907.3
GRC
3941.68(9347)
3941.68:0
29370
0
164114
5526.15 00
GMY
4.94672e+06(5.014e+06)
5.11301e+06:5.95065e+06
0
0
TUR
45568(45568)
45568:1.17982e+06
0
1.7625e+06
0
0
0
654074
0
1980.92
0
FRN
323763(3.525e+06)
487010:0
73133.46225.3
00
0
0
0
0
8038.95
58661.70
81545.365796.1
3470
92744.5 8569.05
54.1764
25877.7
280.7 0
1126
95410.5
721149
0
3200.62
0
242.729
RUM
3964.98(10874)
118654:0
21174.2 0
0899379
0
0
209.371
2174.8
0
0
114054 223615
RUS
225676(4.524e+06)
325772:0
2.10998e+06
0
0
21174.2
0
888055
0
16736
0296.205
2174.8825938
324387
0264.474
2.04864e+06
109033
0
0
0
0183315
3775.06
BUL
11911(11911)
174043:1.18023e+06
543.7 0
132762
0
AUH
1.71612e+06(2.013e+06)
1.75621e+06:2.51203e+06
11059.40
0
17035.15369.31
ITA
24112.1(105871)
164451:0
SWE
22792(22792)
22792:139506
0
72805.1
UKG
614053(4.6514e+06)
685421:0
634.4182015.72
BEL
8912.78(11642)
8912.78:0
64398.7148.502
NOR
6593(6940)
6593:0
POR
5184.8(5614)
69583.5:0
NTH
10145(10145)
10145:11059.4
A Visualization of Europe in World War I
YUG
9741(9741)
14414.5:0
0
0
ALB
1612(1612)
1612:3775.06
DEN
4074.55(4289)
4074.55:0
SPN
104997(110523)
104997:0
4.1
4 EMPIRICAL TESTING
4.1
A Visualization of Europe in World War I
4.1.2
4 EMPIRICAL TESTING
1916
In 1916 the alliance structure had remained largely stable but had undergone some
changes. For instance, between 1914 and 1915, despite allied with Russia, Romania was
also having defense pacts with Germany and Italy. From 1916 onwards, it relinquished the
partnership with Germany and Italy and joined on the UK and France against the Triple
Alliance. Additionally, Turkey also became aligned with Germany against the Entente.
Figure 19: Geopolitics of Europe in 1916
The solution of the game reflects the situation in 1916, characterized by two great battles
on the Western front, at Verdun and Somme, between Germany and the joint armies of France
and Britain. The casualties from Verdun pushed Britain to start the Battle of the Somme
in July 1916, which was part of a multinational plan of the Entente to attack Germany on
different fronts simultaneously. (Prete, 2009; Strachan, 1998)Britain won over Germany in
the battle, which marked the point at which German morale began a permanent decline and
the strategic initiative was lost.
39
4.1
A Visualization of Europe in World War I
4 EMPIRICAL TESTING
Table 4: 1916 Relation
Dyads in War
UK - Germany
UK - Austria-Hungary
UK - Turkey
Belgium - Germany
France - Germany
France - Austria-Hungary
France - Turkey
Germany - Yugoslavia
Germany - Russia
Austria-Hungary - Russia
Austria-Hungary - Yugoslavia
Yugoslavia - Turkey
Russia - Turkey
UK - Bulgaria
France - Bulgaria
Germany - Romania
Germany - Italy
Italy - Bulgaria
Italy - Turkey
Yugoslavia - Bulgaria
Bulgaria - Russia
Bulgaria - Romania
Portugal - Germany
Portugal - Austria-Hungary
Portugal - Bulgaria
Portugal - Turkey
Dyads in Militarized Conflict
UK - The Netherlands
UK - Greece
UK - Sweden
The Netherlands - Germany
Belgium - Austria-Hungary
Belgium - Bulgaria
Belgium - Turkey
Germany - Sweden
Germany - Norway
Germany - Albania
Germany - Greece
Albania - Bulgaria
Albania - Turkey
France - Greece
France - Sweden
Spain - Germany
Austria-Hungary - Albania
Austria-Hungary - Sweden
Albania - Yugoslavia
Albania - Bulgaria
Albania - Turkey
Greece - Bulgaria
Greece - Turkey
Russia - Sweden
40
Dyads in Alliance
UK - Portugal
Germany - Austria-Hungary
France - Russia
Yugoslavia - Greece
Bulgaria - Turkey
Austria-Hungary - Bulgaria
Germany - Bulgaria
Russia - Romania
UK - France
UK - Italy
UK - Russia
France - Italy
Italy - Russia
Germany - Turkey
UK - Romania
France - Romania
Figure 20: 1916 Europe
41
YUG
1319.2(11987)
1319.2:0
984.656
0
5993.5
0
057.2169
0
0
02820.18
SWE
40053(40053)
40053:372755
GRC
12748(12748)
13732.7:123032
0
79.9
351.282
0
0
79.9
0
518.762
TUR
45568(45568)
744057:1.61794e+06
6072.6
0
169912 0
106805
0
595.782
0
985.8
0
146769 0
FRN
100062(4.604e+06)
349967:0
56074.30
284.151145531
16227
0 0
RUM
9415.91(15541)
580328:0
0
0
343655 00
0
3108.2
0
2036.8
0
GMY
2.24373e+06(4.974e+06)
2.24396e+06:4.98345e+06
584288
0
1.63747e+06
3931.04
0
0 390.817
649301 0 0
0
0
0
0 79.9
696453
0
BEL
13684.6(19716)
13684.6:0
0
228.773 1.47069e+06
1.168e+06
90793.2
154706
93862.2
416440
157016
321.369
8940.98 0287472
01.19259e+06
0
32841.40553410
0636109
02411.37
2.1057e+060
0
1.20551e+060 1285
5631310
0
1.0094e+060
883.562
0
32841.4
BUL
9571.34(13298)
1.48026e+06:1.88817e+06
0
0412.8
RUS
518454(4.343e+06)
695699:0
1053.45
54128.2
75949.6
139271
UKG
1.20099e+06(6.2134e+06)
1.49897e+06:0
1461.08
0
AUH
2.445e+06(2.445e+06)
3.00959e+06:3.0144e+06
01186.41
52861.3
1336.66
14738.3
0
032841.4 44.4443
67007.20
0
10502.1957.946
1285
ITA
52790.6(164207)
160738:0
POR
1740.59(6425)
16478.9:0
NTH
17986(17986)
17986:67007.2
NOR
7843.2(8256)
7843.2:0
A Visualization of Europe in World War I
127.367
79.9
ALB
1221.18(1598)
1221.18:47.4668
SPN
115379(121452)
115379:0
DEN
9562(9562)
9562:0
4.1
4 EMPIRICAL TESTING
4.1
A Visualization of Europe in World War I
4.1.3
4 EMPIRICAL TESTING
1917-1918
In 1917, Germany’s military spending peaked within the course of war and surpassed
all of its rivals. Their morale was helped by a series of victories against countries including
Greece, Italy, and Russia and had been at its greatest since 1914 at the end of 1917 and
beginning of 1918 with Russia lapsed into revolution. (Cruttwell, 1934; Herwig, 2014)
1917-1918 saw a major structural change, the US entry, which eventually put an end to
the war. The solution of the game in 1918 would have been entirely different had this factor
not been considered. Actually it was not that Germany did not foresee this to happen. So
Germany also offered a military alliance to Mexico, which outraged the US just as Germany
started defeating the US in submarine warfare. Wilson asked Congress for “a war to end all
wars” and the US declared war on Germany on April 6, 1917.(Link and Wilson, 1954)
Figure 21: Geopolitics of Europe in 1917
Comparing Figure 25 to 24, obviously if it had not been the assistance from the US,
Germany would have been “defensive”, which means that it could have overcome the joint
attacks from the Entente. Paul Kennedy in The Rise and Fall of the Great Powers also noted
42
4.1
A Visualization of Europe in World War I
4 EMPIRICAL TESTING
Table 5: 1917 Relation
Dyads in War
UK - Germany
UK - Austria-Hungary
UK - Turkey
Belgium - Germany
France - Germany
France - Turkey
Austria-Hungary - Italy
Germany - Yugoslavia
Germany - Russia
Austria-Hungary - Russia
Austria-Hungary - Yugoslavia
Yugoslavia - Turkey
Russia - Turkey
UK - Bulgaria
Romania - Turkey
France - Bulgaria
Germany - Romania
Germany - Italy
Italy - Bulgaria
Italy - Turkey
Yugoslavia - Bulgaria
Bulgaria - Russia
Bulgaria - Romania
Portugal - Germany
Portugal - Austria-Hungary
Portugal - Bulgaria
Portugal - Turkey
Germany - Greece
Austria-Hungary - Greece
Austria-Hungary - Romania
Greece - Bulgaria
Greece - Turkey
Dyads in Militarized Conflict
UK - The Netherlands
UK - Greece
UK - Sweden
The Netherlands - Germany
Belgium - Austria-Hungary
Belgium - Bulgaria
Belgium - Turkey
Austria-Hungary - Albania
Germany - Sweden
Germany - Norway
Germany - Albania
Albania - Bulgaria
Albania - Turkey
France - Greece
Spain - Germany
Albania - Bulgaria
Albania - Turkey
Greece - Bulgaria
Greece - Turkey
43
Dyads in Alliance
UK - Portugal
Germany - Austria-Hungary
Germany - Bulgaria
Germany - Turkey
Austria-Hungary - Bulgaria
Bulgaria - Turkey
France - Russia
Yugoslavia - Greece
UK - France
UK - Italy
UK - Russia
France - Italy
France - Italy
UK - Romania
France - Romania
Russia - Romania
4.1
A Visualization of Europe in World War I
4 EMPIRICAL TESTING
Table 6: 1918 Relation
Dyads in War
UK - Germany
UK - Austria-Hungary
UK - Turkey
Belgium - Germany
France - Germany
France - Turkey
Austria-Hungary - Italy
Germany - Yugoslavia
Austria-Hungary - Yugoslavia
Yugoslavia - Turkey
Russia - Turkey
UK - Bulgaria
Romania - Turkey
France - Bulgaria
Germany - Italy
Italy - Bulgaria
Italy - Turkey
Yugoslavia - Bulgaria
Bulgaria - Russia
Bulgaria - Romania
Portugal - Germany
Portugal - Austria-Hungary
Portugal - Bulgaria
Portugal - Turkey
Germany - Greece
Austria-Hungary - Greece
Greece - Bulgaria
Greece - Turkey
France - Austria-Hungary
Dyads in Militarized Conflict
UK - Russia
The Netherlands - Germany
Belgium - Austria-Hungary
Belgium - Bulgaria
Belgium - Turkey
France - Albania
France - Russia
Spain - Germany
Germany - Sweden
Germany - Norway
Germany - Albania
Germany - Russia
Albania - Italy
Italy - Russia
Albania - Bulgaria
Austria-Hungary - Albania
Albania - Yugoslavia
Albania - Turkey
Yugoslavia - Romania
Yugoslavia - Russia
Greece - Russia
Romania - Russia
Russia - Estonia
Russia - Lithuania
44
Dyads in Alliance
UK - Portugal
Germany - Austria-Hungary
Germany - Bulgaria
Germany - Turkey
Austria-Hungary - Bulgaria
Bulgaria - Turkey
Italy - Romania
Yugoslavia - Greece
UK - France
UK - Italy
France - Romania
France - Italy
UK - Romania
4.1
A Visualization of Europe in World War I
4 EMPIRICAL TESTING
Figure 22: Geopolitics of Europe in 1918
the advanced railway system of Germany, which facilitated the transportation of the troops
between the two fronts.(Kennedy, 2010) However, as the morale waned, it would be hard
to predict whether it would have been realistic for Germany to reverse the failing situation
and defeat the Entente. Figure 25 shows the final outcome of the war: the Entente countries
were either powerful or defensive, while Austria-Hungary and Germany were vulnerable.
45
46
Figure 23: 1917 Europe
8394.50
935.4510
0
20.6847
0
2038.28
0
0
3041.29
3971.93
SWE
45922(45922)
45922:64566.4
GRC
34561(34561)
42955.5:98931.1
0
78.35
0590.742
455.05878.35
TUR
45568(45568)
45568:2.20006e+06
6072.6
0
0
3943.2
0
1030.350 1.91588e+06
00
106920 0
982.159
00
0
0
52.5186
2741.86
0
0
BEL
13874.7(19716)
13874.7:6552.33
321.56
0
00
0
37181.5 0
RUS
303368(4.04e+06)
437392:0
27384.90
37182.40
1577.45
0
59006.9
RUM
7597.23(17729)
46564.1:7597.8
146870
0
3545.8
0
00
GMY
7.15e+06(7.15e+06)
7.16828e+06:8.28139e+06
7538.13
985.8
89313.2
8610.57
44710.625070.1
19.85314319.12
0
62841.2
2.9125e+06
00
0
27062.5
33070.31206.02
1.51161e+06
0832.143
3.80023e+06 0801.972
0
853.7652.02e+06
11143.6 00
1.20126e+06
14611.2
3545.8
018277.6
0
2064600
1596
0
BUL
13394(13394)
17599.2:609366
0
0 1108.45
FRN
263024(5.825e+06)
333268:0
164398
53679.1
1596
33615.1
0
38667.9
UKG
1.67294e+06(7.60046e+06)
1.87075e+06:0
0
4205.21
AUH
2.76532e+06(2.862e+06)
2.76532e+06:3.23412e+06
7934.95
102966
19766.9
7002.15
274521130.967
298235
39482.40
0
60552.30
27587.2
0111.068
195.592
ITA
49674.9(197412)
172408:0
POR
3743.99(7980)
278265:32019.1
NTH
17986(17986)
17986:60552.3
NOR
21060.5(22169)
21060.5:0
A Visualization of Europe in World War I
YUG
418.499(16789)
418.499:0
ALB
1337.1(1567)
1337.1:376.708
SPN
115379(121452)
115379:0
DEN
11589(11589)
11589:0
4.1
4 EMPIRICAL TESTING
0
761.4
4312.95
0
0
6770.65
329.352
0
Figure 24: 1918 Europe (Without US Entry)
47
ALB
1545(1545)
1545:9914.57
0
0
34.3033
0
0 09550.91
4029
0
33.2873
8046.4
0
DEN
13947(13947)
13947:0
0
114472
159.315
9657.38
76.5228
0
0
0
0
0
0
224968
ITA
34728(228943)
64310.5:0
125231 93610
294.656
GRC
3073.09(40232)
3232.4:0
0
0
674.376
2611.06
0
1.31504e+06
RUM
9452.47(20974)
132418:0
1.05025e+06
0
694.354
0
1801.4
NTH
23102.1(24318)
23102.1:0
4420.33
1007.250 7889.12
979.347
1048.7
0
4.05213e+060
8046.4
0 1779.1
0
227.89295639.4
615246
1353.49
045788.6
1801.4
1801.4
31.6142
4194.80
FRN
1.30217e+06(7.708e+06)
1.42861e+06:0
YUG
528.155(20145)
10185.5:41.45
0 430.704
0
1215.9 0
1.45837e+06
21192.5 198771
182.889 0
BUL
14337(14337)
575322:1.52601e+06
2145.83
0
0
AUH
2.133e+06(2.133e+06)
2.133e+06:2.57237e+06
4976.81
520.168
0
730.2780 3.854e+06
6667.69
06904.46
00
362.086
560646
463029
0
0
0.00124404
338.889
5624
0
0
0
586.862
GMY
8.06122e+06(8.779e+06)
8.06124e+06:8.05317e+06
24.1867
157136
TUR
44864.2(48820)
202000:1.11328e+06
62.51131406
0
1197.2
19082.3511.166
02011.6
0
8818.41
0
1048.7
26651.5
244.547
RUS
258741(258741)
258741:459852
2226340
UKG
620673(8.10426e+06)
715105:0
57317.8
66.2802
POR
2842.17(9007)
60159.9:0
A Visualization of Europe in World War I
NOR
14466.6(15228)
14466.6:0
SWE
81946.1(86259)
81946.1:0
SPN
128642(135413)
128642:0
BEL
19305.9(28120)
19305.9:0
4.1
4 EMPIRICAL TESTING
415.3732471.3
26669.4
0
1309.25
0
0
0
1.23417e+06
0
1048.7
1007.25
GRC
11872.7(40232)
12288.1:0
2834.460
0
5512.01
3678100
00
04029
654.707
72370.8
1.36183e+06
626740
0
0
4029
0
Figure 25: 1918 Europe (With US Entry)
0
3.854e+060
5707.3
0
1406
8046.4
0
464.736
0
48
12029.6 93077.6
0
0
5624
0
0
948.206
0
1969.63
1191.4 0
869.712
0
174654
308.155
274680 0
102115
1668.81
0
1215.9
0
1048.7
0114472
0
ITA
36454.1(228943)
232517:0
0 105795
0
602.197
BUL
14337(14337)
464398:1.45253e+06
NTH
23102.1(24318)
23102.1:0
706073
0 0
1801.4 11666.30
23697.8
0
450061
0
0
1801.4
GMY
7.87642e+06(8.779e+06)
7.87642e+06:9.45367e+06
3939.57
02454.17
4.05213e+06
0
UKG
1.09919e+06(8.10426e+06)
1.31965e+06:0
0
1007.25
0
637549224085
00
0
0
AUH
2.133e+06(2.133e+06)
2.13545e+06:3.44198e+06
2610411242.8
24127.9
RUM
7975.01(20974)
342578:0
450061
0
338971217242
0
7330.2
0 0
6770.65
0
0 1406
493143
0
1.40285e+06
0
4194.8
0
FRN
1.21623e+06(7.708e+06)
1.56789e+06:0
0 0
TUR
48820(48820)
498881:2.26305e+06
1.40285e+06
0
BEL
18735.8(28120)
18735.8:0
0
0
POR
4029.11(9007)
178683:0
04312.95
761.4
0
3635.66
0
0
0
DEN
13947(13947)
13947:0
RUS
258741(258741)
258741:388136
SWE
81946.1(86259)
81946.1:0
NOR
14466.6(15228)
14466.6:0
A Visualization of Europe in World War I
YUG
2720.27(20145)
5191.57:41.45
0
115.601
ALB
1545(1545)
1545:26785
USA
2.48123e+06(7.01423e+06)
2.48123e+06:0
SPN
128642(135413)
128642:0
4.1
4 EMPIRICAL TESTING
4.1
A Visualization of Europe in World War I
4.1.4
4 EMPIRICAL TESTING
Simulation Results
Having obtained 10,000 possible solutions of the game from simulation, I present Table 7,
which shows the probability of being defensive, powerful and vulnerable for selected countries
in World War I.
Table 7: Probability of Being in Different States for Selected Countries from 1914-1918
Country-Year
Germany-1914
Germany-1915
Germany-1916
Germany-1917
Germany-1918 (N/A USA Entry)
Germany-1918 (With USA Entry)
Austria-Hungary-1914
Austria-Hungary-1915
Austria-Hungary-1916
Austria-Hungary-1917
Austria-Hungary-1918 (N/A USA Entry)
Austria-Hungary-1918 (With USA Entry)
UK-1914
UK-1915
UK-1916
UK-1917
UK-1918 (N/A USA Entry)
UK-1918 (With USA Entry)
France-1914
France-1915
France-1916
France-1917
France-1918 (N/A USA Entry)
France-1918 (With USA Entry)
Russia-1914
Russia-1915
Russia-1916
Russia-1917
Russia-1918 (N/A USA Entry)
Russia-1918 (With USA Entry)
Pr(Vulnerable)
91.2%
94.53%
97.56%
98.23%
0%
97.92%
98.2%
99.8%
99.69%
98.18%
100%
99.99%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
100%
100%
Pr(Defensive)
8.76%
5.47%
2.44%
1.77%
100%
2.08%
1.8%
0.2%
0.31%
1.82%
0%
0.01%
10.51%
6.05%
2.98%
3.59%
100%
2.09%
10.51%
6.05%
2.98%
1.77%
100%
2.09%
10.51%
6.05%
2.98%
3.59%
0%
0%
Pr(Powerful)
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
0%
89.49%
93.95%
97.02%
96.41%
0%
97.91%
89.49%
93.95%
97.02%
98.23%
0%
97.91%
89.49%
93.95%
97.02%
96.41%
0%
0%
Several regularities can be observed: (1) the likelihood of failure persistently increases for
Germany; (2) without the entry of the US, Germany could have been defensive; (3) Russia’s
domestic revolution and later withdrawal from the war greatly impaired its prospect for
49
4.2
A Visualization of the World in World War II
4 EMPIRICAL TESTING
retaining a powerful state; (4) The entry of the US helped the Entente to end the war.
Obviously, these regularities are consistent with historic facts.
4.2
A Visualization of the World in World War II
The model and algorithm work even better with the case of World War II that manifests
even more complex relation patterns and encompasses much greater geographical scale than
World War I. The alliance dynamics in the period from 1939 to 1945 are mainly between
the Axis (Germany, Italy, Japan, Hungary, Romania, Bulgaria) and the Allies (U.S., Britain,
France, USSR, Australia, Belgium, Brazil, Canada, China, Denmark, Greece, Netherlands,
New Zealand, Norway, Poland, South Africa, Yugoslavia).(Amt, 1948)
The model confirms the major historic events from 1939 to 1945, especially:
Fact 1: The 1939 Appeasement. With the nonaggression pacts signed by the Soviet
Union and Germany, Germany quickly conquered Poland, then defeated Britain and France
with large advantages.
Fact 2: Massive Successes of Germany in Western Europe in 1940. 1940 saw
Germany invade and defeat nearly all of the Western Europe.
Fact 3: Turning Point at the Eastern Front in 1941. The Battle of Moscow between
the Soviet Union and Germany marks the beginning of the loss of advantages for Germany.
Fact 4: Turning Point in the Asia-Pacific in 1942. The US greater involvement in
the war after the Pearl Harbor attack marks the turning point of the war.
Fact 5: The Allied Victory. From 1943 to 1945, the joint efforts by the Allies overwhelmed that of the Axis.
4.2.1
1939
Though the Soviet Union joined the Allies after being attacked by Nazi Germany in 1941,
it began World War II with non-aggression pacts with Nazi Germany. The nonaggression
pacts, along with the other secret protocols, divided the whole of Eastern Europe into German
and the Soviets spheres of influence. (Amt, 1948).
50
4.2
A Visualization of the World in World War II
4 EMPIRICAL TESTING
Figure 26: 1939 Europe
Figure 27 shows that under the attacks by Nazi Germany and the Soviet Union, Poland
was vulnerable. Though was requested by Poland for military assistance, France and Britain
did not immediately declare war on Germany. Warsaw surrendered soon after and Germany
gained a swift victory. Figure 27 also shows the outcome of the Sino-Japanese war on the
Asia-Pacific battlefield. Due to great advantages over China, Japan held a winning position
in 1939. Comparatively speaking, the Axis powers won over the Allies in 1939.
51
4.2
A Visualization of the World in World War II
4 EMPIRICAL TESTING
Table 8: 1939 Relation
Dyads in War
China - Japan
Russia - Finland
Russia - Japan
Russia - France
Russia - United Kingdom
Germany - United Kingdom
Germany - Belgium
Germany - France
Germany - Poland
Germany - Australia
Germany - New Zealand
Germany - Canada
Germany - South Africa
Mongolia - Japan
Dyads in Militarized Conflict
Spain - Poland
Spain - Italy
United Kingdom - Netherlands
United Kingdom - Japan
United Kingdom - Italy
United Kingdom - Uruguay
Russia - Estonia
Russia - Poland
Russia - Latvia
Russia - Afghanistan
Italy - Albania
France - Italy
France - Japan
Hungary - Romania
Poland - Estonia
United States - Germany
United States - United Kingdom
Germany - The Netherlands
Germany - Belgium
Germany - Luxemburg
Germany - Finland
Germany - Latvia
Germany - Sweden
Germany - Estonia
Germany - Russia
Germany - Mexico
Germany - Uruguay
Germany - Argentina
Germany - Norway
Germany - Lithuania
Germany - Italy
Germany - Spain
Germany - Switzerland
Germany - Czechoslovakia
52
Dyads in Alliance
United Kingdom - Egypt
United Kingdom - France
United Kingdom - Yugoslavia
United Kingdom - Greece
United Kingdom - Iraq
United Kingdom - Bulgaria
United Kingdom - Romania
United Kingdom - Turkey
United Kingdom - Portugal
United Kingdom - Poland
France - Yugoslavi
France - Greece
France - Bulgaria
France - Romania
France - Turkey
France - Egypt
France - Poland
Russia - France
Russia - Turkey
Russia - Egypt
Russia - Iran
Russia - Estonia
Russia - Latvia
Russia - Lithuania
Russia - Czechoslo
Russia - Mongolia
Bulgaria - Romaniav
Bulgaria - Russia
Bulgaria - Turkey
Bulgaria - Egypt
Romania - Russia
Romania - Egypt
Romania - Poland
Romania - Czechoslo
Romania - Yugoslavia
Germany - Italy
Italy - Albania
Greece - Romania
Greece - Turkey
Greece - Bulgaria
Greece - Russia
Greece - Egypt
Yugoslavi - Greece
Yugoslavi - Turkey
Yugoslavi - Bulgaria
Yugoslavi - Russia
Yugoslavi - Egypt
Latvia - Estonia
Turkey - Romania
Turkey - Egypt
Figure 27: 1939 Europe
53
CHN
173755(173755)
173755:218390
9361.42
78939.8
32.5406
1389
1368.74
6713
AFG
1000(1000)
1000:21567.5
UKG
100809(7.89567e+06)
1.02703e+06:1.02326e+06
2893.05
4108.2
0653327 379111.3856
BUL
10313.2(18955)
29597.6:0
URU
3571(3571)
3571:3573.1
185.726
470836
11874.2
8.44507
1.19682e+06
1.55602e+06 339994
1341.14
16432.80.0800508
169381
1698.91
563.618
POL
912679(968472)
1.56933e+06:1.56772e+06
TUR
10295.2(59371)
22234.8:0
699.58 84.7235
21567.50
9.36041
19702.8
13005.6
34.368
8525.02
CZE
203969(268742)
218613:94703.7
256.15
13879.1
6300.87
3870.98
1155.12
765.237
38330.4
ROM
16233.6(82164)
73039.2:0
1618.21
8378.96
285.952
1912.61
55092.5
3.63237e+06
1.01203e+06
YUG
26539.5(98514)
47269.6:0
124336
125.855
421.6
35993.4
13437.1
108141
116387
256.15
LIT
10237.1(11230)
76809.4:61479.1
561.5
62040.6
GMY
94081.3(1.2e+07)
227964:227735
0.714755
133882
0
125700
CAN
125700(125700)
125700:125700
ITA
397288(669412)
398685:356698
18600.1
0
MEX
18600(18600)
18600:18600.1
BEL
63255(63255)
63255:63255.1
0
63255.1
66572.3
431.409
0
6890
299206
72089.1
80128.6
EST
4003.38(5123)
129193:119746
46544.7
4123.15
4123.15
33470.6
NTH
114233(114233)
114233:114247
RUS
118394(5.98412e+06)
148280:0
4052.65
5281.451878.02 6098.58
1744.23
9086.23
6.21109e+06
5.18784e+06
8.52993
598412
6875.48
951.284
19702.8
33470.6
6153.71
3249.26
57.2071
853.291
EGP
5905.05(11914)
23507.6:0
7704.67 7711.76
398.199
677.472 3097.51
824.63
33470.6390168
75.6275
87858.4
9182.07
9800
SPN
73392.1(82463)
73392.1:71769
21887.5
481.469
2514.14
4.3698
0
LAT
7081.48(8432)
95421.3:79707
GRC
23399.6(49784)
61265.7:0
0
668610
1.19682e+06
12.8675
2874.95
16432.86.63282
6377.36
1658.07
2382.8
3.55638
869124
13.6687
9956.8
0.62524
8189.75
41.6442
2382.8
6790.66
3300.86
13.4489
16432.8
11874.2
3.93939
FRN
790278(1.02365e+06)
3.61166e+06:3.60994e+06
73.3279
382.898
1801.27
7.22308
1073570
0.0312854
0
MON
3000(3000)
671610:653327
1039.64
6462.41
131.723
3374.23
6.49645
460.873297.983
0.67672
0
3568.73
0
672687
USA
970200(980000)
970200:0
4937.05
94602.7
3421.05
65111
975.0020
22861.4 1396.8
41256
0
SWE
93804(98741)
93804:89665.7
2949.2
0
8322.4
NOR
64999.9(68421)
64999.9:61690
14968.6
0
LUX
975(975)
975:975.002
0
67076.1
57038.4
7080.060
ABL
5587.2(6984)
28448.6:0
SWI
41256(41256)
41256:41256
SAF
8322(8322)
8322:8322.4
ALB
6984(6984)
6984:14968.6
ARG
56034.8(58984)
56034.8:54089.2
NZL
7080(7080)
7080:7080.06
AUL
67076(67076)
67076:67076.1
A Visualization of the World in World War II
0
218390
JPN
976968(1.69997e+06)
976968:926409
IRQ
5556(6945)
5588.54:0
HUN
54968(57861)
54968:1215.15
FIN
68491(68491)
68491:672687
4.2
4 EMPIRICAL TESTING
4.2
A Visualization of the World in World War II
4.2.2
4 EMPIRICAL TESTING
1940
Table 9 indicates wars between Germany and Western Europe including France and
Britain as well as Scandinavian countries like Norway. Originally Hitler had intended to
respect Norways neutrality but still invaded Norway in 1940. In Western Europe, Germany’s
sweeping victory led to an occupation of the Netherlands, Belgium and France and to a
British evacuation from Dunkirk(Klemann and Kudryashov, 2012).
Figure 28: 1940 Europe
Despite being shown on the graph at the same time, the war between Germany and
Britain happened after France was conquered. Germany lay down a plan of attack to destroy
British air power and so open the way for the amphibious invasion. However, the victory by
the Royal Air Force (RAF) Fighter Command blocked this possibility (Weinberg, 1994).
In this year, the collapse of France convinced Mussolini that the time to implement his
Pact of Steel with Hitler had come, and on June 10, 1940, Italy declared war against France
and Britain. (Knox, 1986) Soon France was conquered and Germany entered Paris on June
14th, 1940 (Paxton, 2001).
Results of the game show the follows: first, France was vulnerable mainly because of the
joint attacks from Germany and Italy; Britain was simultaneously engaged in several conflicts
54
4.2
A Visualization of the World in World War II
4 EMPIRICAL TESTING
Table 9: 1940 Relation
Dyads in War
China - Japan
Russia - Finland
United Kingdom - Japan
United Kingdom - Italy
United Kingdom - France
Germany - United Kingdom
Germany - Belgium
Germany - France
Germany - Norway
Germany - Australia
Germany - New Zealand
Germany - Canada
Germany - Greece
Germany - The Netherlands
Italy - Greece
Dyads in Militarized Conflict
Spain - France
Spain - United Kingdom
United Kingdom - France
United Kingdom - Japan
United Kingdom - Norway
United Kingdom - Denmark
United Kingdom - Italy
United Kingdom - Switzerland
United Kingdom - Sweden
United Kingdom - Romania
United Kingdom - Yugoslavia
United Kingdom - Portugal
United Kingdom - Russia
United Kingdom - Brazil
United States - Romania
United States - Germany
United States - United Kingdom
United States - Romania
Germany - Ireland
Germany - The Netherlands
Germany - Belgium
Germany - Luxemburg
Germany - Finland
Germany - Latvia
Germany - Sweden
Germany - Estonia
Germany - Norway
Germany - Yugoslavia
Germany - Uruguay
Germany - Argentina
Germany - Russia
Germany - Romania
Germany - Italy
Germany - Turkey
Germany - Bulgaria
Germany - Panama
Germany - Hungary
Germany - Portugal
Russia - Romania
Russia - Turkey
Russia - Latvia
Russia - Lithuania
Russia - Estonia
Russia - Afghanistan
Russia - Bulgaria
Italy - Yugoslavia
Italy - France
Italy - Spain
Italy - Turkey
Italy - Iran
Italy - Egypt
Italy - Panama
Italy - Sweden
Italy - Greece
55
Dyads in Alliance
United Kingdom - Egypt
United Kingdom - France
United Kingdom - Iraq
United Kingdom - Turkey
United Kingdom - Portugal
France - Turkey
Russia - Iran
Russia - Czechoslovakia
Russia - Mongolia
Russia - Estonia
Russia - Latvia
Russia - Lithuania
Germany - Japan
Germany - Hungary
Germany - Romania
Germany - Italy
Romania - Turkey
Romania - Italy
Romania - Hungary
Romania - Japan
Italy - Hungary
Italy - Japan
Greece - Romania
Greece - Turkey
Turkey - Egypt
Yugoslavi - Greece
Yugoslavi - Romania
Yugoslavi - Turkey
Yugoslavi - Russia
Latvia - Estonia
Figure 29: 1940 Europe
56
00
0
0
BUL
34517(34517)
34517:144860
0
298708
30326.24381.05
276252
0
0
265783
5960.72
0
ITA
5606.11(606523)
8249.03:0
01636.83
SWE
105623(105623)
105623:120534
2318.34
694.856
18464.8
00
0
33.8224
16432.8
21006.50 0
0
5.85551e+06
TUR
79176(79176)
119900:256178
0
00
015323.9
3906.57
00
75246.4
0
0
CHN
217584(217584)
217584:232379
UKG
9.94833e+06(9.94833e+06)
9.9497e+06:1.05245e+07
0
67596.3
04381.05
13888.6
0
429637
0
0
0 0
1370.2
0
0
4381.05
0
SPN
74477.8(87621)
74477.8:25945.1
IRQ
5480.8(6851)
5480.8:0
FRN
5.70776e+06(5.70776e+06)
5.70776e+06:5.87378e+06
POR
31024(31024)
31024:75246.4
0
2431.65
URU
3571(3571)
3571:43013.9
114574
0
HUN
50285.8(57861)
69161.2:0
822.423
1.14823
30326.2
6072.8
ROM
33380.7(82164)
390131:381894
0
IRN
20324.9(24250)
45626.6:29113.7
232379
0
0
3744.4
AFG
1000(1000)
1000:1043.04
18180.6 5256.83
117.829
257833
289.608
200.57
3341.42
10498.5
2364820
16400.3
6464.84
0
1.60934e+06
0
4108.2
82850
1799.3
0
212000
16570
CZE
214994(268742)
224352:0
815290398.69
1968.2
21437.8
49.544
729192
756766
0
81427678.9672
JPN
12537.2(1.86318e+06)
15559.2:0
830863
241.15
RUS
807201(6.14521e+06)
866793:752739
FIN
89744(89744)
89744:1.61581e+06
2685.24
3231.64
9358.47
30726153748.4
1.06e+06
874982
434.467
2712.56
0
PAN
43(43)
43:18785.1
25950.6
600
MON
2400(3000)
28350.6:0
25301.6
GMY
87173.2(2.12e+07)
96684.7:0
911867
1043.04 6072.8
0
218.9569954.1
YUG
44268.2(121456)
922592:930048
228848024291.2
3072614108.2
0 01.54479e+06
46799.5
0
2384.760
2856960
0
87703.2
98060.5
0
08.2426e+06
0
24291.2
25692.3
0
30326.2
1212.5
0
16432.8
5526.88
0
GRC
62145(62145)
102869:257488
43013.9
EGP
14354(14354)
14354:15323.9
ARG
69908(69908)
69908:87703.2
LIT
7872.8(9841)
29310.6:0
USA
1.55758e+06(1.657e+06)
1.55758e+06:195430
112758
0
1257960
349959
0
LAT
6190.99(7984)
736110:814891
726.725
1344.77
EST
3776.16(4823)
819397:830622
BRA
71143.6(74888)
71143.6:0
DEN
34186.7(35986)
34186.7:0
NOR
89338(89338)
89338:112758
IRE
17684(17684)
17684:125796
NTH
168422(168422)
168422:349959
CAN
730100(730100)
730100:756766
A Visualization of the World in World War II
NZL
9836(9836)
9836:276252
AUL
179418(179418)
179418:265783
LUX
1168(1168)
1168:67596.3
BEL
289421(289421)
289421:298708
SWI
46201.3(48633)
46201.3:0
4.2
4 EMPIRICAL TESTING
4.2
A Visualization of the World in World War II
4 EMPIRICAL TESTING
with countries including Germany, Russia and Brazil. Facing the attacks on multiple fronts,
Britain was also predicted to be “vulnerable”; accordingly, both Germany and Italy were
defensive, though not yet powerful in this year. Generally speaking, the game predictions
largely support the key historic facts in this period.
4.2.3
1941
In 1941, Germany launched attacks in the Balkans and Yugoslavia and Greece surrendered. In addition, this year has the following events: the Germany-Soviet Union alignment
broke down and Germany attacked the Soviet Union, Japan attacked Pearl Harbor, the US
and Britain declared war on Japan, and Germany and Italy entered into conflict with the
US. With continental Europe under Nazi’s control, the war took on a more global dimension
in this year.
Figure 30: 1941 Europe
While the conflict with Britain continued, Germany invaded Russia executing what was
known as “Operation Barbarossa” on June 22. The initial advance was swift and Moscow
coming under attack at the end of the year. The bitter Russian winter, however, crippled
the German advance. The Soviets counterattacked in December successfully and the So-
57
4.2
A Visualization of the World in World War II
4 EMPIRICAL TESTING
Table 10: 1941 Relation
Dyads in War
China - Japan
United Kingdom - France
United Kingdom - Japan
United Kingdom - Italy
United Kingdom - Bulgaria
United Kingdom - Romania
Germany - Canada
Germany - Yugoslavia
Germany - Greece
Germany - Australia
Germany - New Zealand
Germany - Russia
Germany - South Africa
Germany - United Kingdom
Hungary - Russia
United States - Germany
United States - Italy
United States - Japan
Italy - Yugoslavia
Italy - Greece
Greece - Bulgaria
Russia - Romania
Russia - Finland
Russia - Japan
Japan - South Africa
Japan - Australia
Japan - New Zealand
France - Thailand
Dyads in Militarized Conflict
Spain - Russia
United Kingdom - Hungary
United Kingdom - France
United Kingdom - Finland
United Kingdom - Norway
United Kingdom - Germany
United Kingdom - Iraq
United Kingdom - Bulgaria
United Kingdom - Greece
United States - Hungary
United States - Bulgaria
United States - Japan
United States - Germany
United States - Romania
Germany - Haiti
Germany - Nicaragua
Germany - Costa Rica
Germany - Cuba
Germany - Dominica
Germany - Salvador
Germany - Guatemala
Germany - Honduras
Germany - Panama
Germany - Yugoslavia
Germany - Sweden
Germany - Russia
Germany - Romania
Germany - Turkey
Germany - Bulgaria
Germany - Egypt
Germany - Portugal
Yugoslavia - Bulgaria
Yugoslavia - Romania
Romania - South Africa
Romania - Australia
Romania - New Zealand
Romania - Nicaragua
Romania - Haiti
Romania - Hungary
Russia - Romania
Russia - Iran
Russia - Bulgaria
Bulgaria - Nicaragua
Bulgaria - Hungary
Bulgaria - Haiti
Bulgaria - Turkey
Bulgaria - Canada
Italy - Haiti
Italy - Nicaragua
Italy - Costa Rica
Italy - Cuba
Italy - Dominica
Italy - Salvador
Italy - Guatemala
Italy - Honduras
Italy - Panama
Japan - Thailand
Japan - Nicaragua
Japan - Haiti
Japan - Costa Rica
Japan - Cuba
Japan - Dominica
Japan - Salvador
Japan - Guatemala
Japan - Honduras
Japan - Panama
Hungary - Haiti
Hungary - Nicaragua
Hungary - Yugoslavia
58
Dyads in Alliance
United Kingdom - Egypt
United Kingdom - Russia
United Kingdom - Turkey
United Kingdom - Iraq
United Kingdom - Portugal
Hungary - Italy
Hungary - Bulgaria
Hungary - Romania
Hungary - Japan
France - Yugoslavia
France - Greece
France - Bulgaria
France - Romania
France - Turkey
France - Egypt
France - Poland
Russia - Czechoslovakia
Russia - Mongolia
Russia - Iran
Germany - Hungary
Germany - Bulgaria
Germany - Romania
Germany - Japan
Germany - Italy
Italy - Bulgaria
Italy - Romania
Italy - Japan
Bulgaria - Japan
Romania - Bulgaria
Romania - Japan
Japan - Thailand
59
Figure 31: 1941 Europe
USA
6.301e+06(6.301e+06)
6.301e+06:6.34825e+06
0
3017.28
01980.16
0
108248
2125.1
0
0956.985
585983
0
0
258740
91.5786
0
44472.6
THI
423.779(21856)
75920.8:64940.2
5.64637e+06
376429
0
0
507.761
NIC
844(844)
844:51608.1
0
891.228
0
0
0
5780.05
ITA
10976.7(541238)
99569:0
80853.4
0
YUG
179324(179324)
300328:1.49087e+06
5081.01
HAI
1509(1509)
1509:23161.7
0
0
121004
0
1423.7
1725.85 0
19502.30
03821.88
0.12107
75497
01.32925
3.10454
112.137
0
CUB
4000(4000)
4000:12857.1
046267.6
1894.67
87795.6
06443.01
0
211.583
441274
0
126.655
0
34010
0
0
559.438
PAN
636(636)
636:29926.9
1410.62
0
909.288
3835.39
66.5336
028942.1
0
43499
00
22730.3
38.8094
0
0
4691.6
0
208789
0
1147.090
0
4711.54
23646.1101.854
1371.49
0
0
97769.6
SAF
112840(112840)
112840:252326
6.92658
149.971
1608200
0
4673.37
0
0
0
2284.37
40.49120
0
1370.2
700758
0
114426
0
HUN
1131.37(110555)
29037.9:0
04850
FIN
70374(93832)
70374:0
018766.4
RUS
6.88423e+06(6.88423e+06)
6.88968e+06:7.00113e+06
170509
BUL
301.393(34517)
26162.1:0
37.9378
0
46.6488
92.1471
088657.7
0
POR
36211(36211)
36211:88657.7
6.8774e+06
0
27583.7
0
121004
1540.440
0
0
GMY
171016(2.89e+07)
182063:0
0
1.08717e+07
2389.69
17.9432
95.2393
1455.84
ROM
28.8735(10213)
5048.68:0
275701
0
11.3575
52.794
UKG
1.13e+07(1.13e+07)
1.13014e+07:1.26477e+07
CHN
244000(244000)
244000:286456
0
7742.9
0
0
0286456
98.2716
3302.73
8994.41
0 827.913 0
0 4990.36
414.504
5.508812409.81
242.449
182.886
0
00
817.574
165763
TUR
108253(108253)
229257:276610
0
1.39712e+060
8.7216233.6134
121004
0
JPN
57168.1(2.92992e+06)
60723.1:0
1558.05
152.888
0
067.9073
0
155.105
12700.2
0
FRN
515.092(605022)
548.705:0
0 300209
121004
0
156.788
0
1.40968e+06
52.4464
0
0
5415.66
84.9114398.292
86372.321432.1
0
4747.64
5.56251
GRC
79821(79821)
200825:461594
SWE
148721(148721)
148721:165763
URU
1000(1000)
1000:0
EGP
17798(17798)
138802:160820
IRN
19400(24250)
19400:0
0
1699.11
0
12519.5
600 0
COS
630(630)
630:120548
3051.46
0
0
0
37551.5
4500.35 0
1.0676e+06
IRQ
5480.8(6851)
5480.8:0
0
1107.85
MON
2400(3000)
2400:0
NZL
120750(120750)
120750:871308
SAL
1650(1650)
1650:6122.07
CAN
1.03838e+06(1.03838e+06)
1.03838e+06:1.06871e+06
DOM
1800(1800)
1800:52355.3
SPN
85506.6(90007)
85506.6:0
A Visualization of the World in World War II
HON
1170(1170)
1170:47409.7
GUA
2000(2000)
2000:10922.4
AUL
550072(550072)
550072:635260
SWI
55174(55174)
55174:0
4.2
4 EMPIRICAL TESTING
4.2
A Visualization of the World in World War II
4 EMPIRICAL TESTING
viet counteroffensives were even counted as one of the greatest turning points in the entire
war.(Fugate, 1984)
In the Asia-Pacific, Japan mounted a surprise attack on the US Navy base of Pearl Harbor
in Hawaii on December 7. (Weinberg, 1994) With Germany declaring war on the US, more
conflicts ensued and led to the Pacific war.
The solution of the game in Figure 31 illustrates the defeat of the US under the attacks
by Japan and Germany (low willingness parameter caused by little involvement in the war),
the massive victory of Germany in Europe and also Japan’s success in other Asia-Pacific
areas. Though the battle of Moscow had crushed the German offensive against the Soviet
Union, its effects did not become pronounced in this year. In other words, the Soviet Union
was still vulnerable in the Soviet-German conflict.
4.2.4
1942 - 1943
The US declared war on Japan and assisted Britain in the air battles with Germany in
1942. In the Pacific, June saw the peak and swift decline of Japanese expansion, because of
the Battle of Midway, in which US sea-based aircraft destroyed four Japanese carriers and a
cruiser and which marked the turning point in the Pacific War. (Weinberg, 1994)
The year of 1942 also saw a reversal of German fortunes. British forces under Montgomery
gained the initiative in North Africa at El Alamein, and Russian forces counterattacked at
Stalingrad. (Weinberg, 1994) Each of the two battles proved itself to be the respective turning
point in the North African and the European fields.
The solutions in Figure 34 and Figure 35 shows the vulnerability of Germany, Italy and
Japan and the powerful states of the Allies including the US, Britain and the Soviet Union in
these two years. German surrendered to the Soviet armies in February 1943 at Stalingrad. In
mid-May German and Italian forces in North Africa surrendered to the Allies, who invaded
Sicily in July. In the Asia-Pacific, the US forces defeated the Japanese army at Guadalcanal.
60
4.2
A Visualization of the World in World War II
Figure 32: 1942 Europe
Figure 33: 1943 Europe
61
4 EMPIRICAL TESTING
4.2
A Visualization of the World in World War II
4 EMPIRICAL TESTING
Table 11: 1942 Relation
Dyads in War
China - Japan
United Kingdom - France
United Kingdom - Japan
United Kingdom - Italy
United Kingdom - Bulgaria
United Kingdom - Romania
Germany - Canada
Germany - Russia
Germany - Australia
Germany - New Zealand
Germany - South Africa
Germany - United Kingdom
Hungary - Russia
United States - France
United States - Germany
United States - Italy
United States - Japan
Russia - Romania
Russia - Finland
Russia - Japan
Japan - South Africa
Japan - Australia
Japan - New Zealand
Dyads in Militarized Conflict
Spain - Russia
United Kingdom - Hungary
United Kingdom - Egypt
United Kingdom - Finland
United Kingdom - Thailand
United Kingdom - Germany
Canada - Japan
Ecuador - Peru
Thailand - Australia
United States - Hungary
United States - Bulgaria
United States - Romania
Germany - Brazil
Germany - Argentina
Germany - Haiti
Germany - Nicaragua
Germany - Costa Rica
Germany - Cuba
Germany - Dominica
Germany - Salvador
Germany - Guatemala
Germany - Honduras
Germany - Panama
Germany - Ethiopia
Germany - Sweden
Germany - Mexico
Germany - Chile
Germany - Uruguay
Romania - South Africa
Romania - Australia
Romania - New Zealand
Romania - Nicaragua
Romania - Haiti
Bulgaria - Nicaragua
Bulgaria - Haiti
Bulgaria - Canada
Italy - Brazil
Italy - Mexico
Italy - Ethiopia
Italy - Haiti
Italy - Nicaragua
Italy - Costa Rica
Italy - Cuba
Italy - Dominica
Italy - Salvador
Italy - Guatemala
Italy - Honduras
Italy - Panama
Italy - Sweden
Japan - Mexico
Japan - Ethiopia
Japan - Nicaragua
Japan - Haiti
Japan - Costa Rica
Japan - Cuba
Japan - Dominica
Japan - Salvador
Japan - Guatemala
Japan - Honduras
Japan - Panama
62
Dyads in Alliance
United Kingdom - Egypt
United Kingdom - Russia
United Kingdom - Turkey
United Kingdom - Iraq
United Kingdom - Portugal
United Kingdom - Iran
Russia - Czechoslovakia
Russia - Mongolia
Russia - Iran
Germany - Italy
Japan - Thailand
4.2
A Visualization of the World in World War II
4 EMPIRICAL TESTING
Table 12: 1943 Relation
Dyads in War
China - Japan
United Kingdom - France
United Kingdom - Japan
United Kingdom - Italy
United Kingdom - Bulgaria
United Kingdom - Romania
Germany - Italy
Germany - Russia
Germany - Australia
Germany - New Zealand
Germany - South Africa
Germany - United Kingdom
Hungary - Russia
United States - France
United States - Germany
United States - Italy
United States - Japan
Russia - Romania
Russia - Finland
Russia - Japan
Japan - South Africa
Japan - Australia
Japan - New Zealand
Italy - Bulgaria
Dyads in Militarized Conflict
Spain - Russia
United Kingdom - Hungary
United Kingdom - Egypt
United Kingdom - Finland
United Kingdom - Thailand
United Kingdom - Germany
Canada - Japan
Canada - Bulgaria
Thailand - Australia
United States - Hungary
United States - Bulgaria
United States - Romania
Germany - Iraq
Germany - Saudi Arabia
Germany - Switzerland
Germany - Nicaragua
Germany - Colombia
Germany - Brazil
Germany - Iran
Germany - Bolivia
Germany - Ethiopia
Germany - Italy
Germany - Sweden
Germany - Spain
Germany - Panama
Germany - Egypt
China - Mongolia
China - Russia
Romania - South Africa
Romania - Australia
Romania - New Zealand
Russia - Sweden
Italy - Iraq
Italy - Thailand
Italy - Brazil
Italy - Bolivia
Italy - Ethiopia
Italy - United States
Italy - United Kingdom
Japan - Iraq
Japan - Saudi Arabia
Japan - Bolivia
Japan - Ethiopia
63
Dyads in Alliance
United Kingdom - Egypt
United Kingdom - Russia
United Kingdom - Turkey
United Kingdom - Iraq
United Kingdom - Portugal
United Kingdom - Iran
Russia - Czechoslovakia
Russia - Mongolia
Russia - Iran
Germany - Italy
Japan - Thailand
Figure 34: 1942 Europe
64
1.872e+06
0
1012820
0
57907
402.664600
0
216296
0
107004
0
BRA
114550(127278)
114550:0
USA
109966(2.6e+07)
109966:0
594764
0
43038.1
IRN
19144.6(24250)
26382.2:0
571.774850
6665.89
255.418
0
232.295
0
2.60953e+06
10605.5
CHI
39235(41300)
39235:0
6363.9
3420.42
0
6363.90
1.99474e+07
225841
0
0
9.76212e+06
42.2
2088.01
0
2065
0
0
0
0
0
0
0
0
0
GUA
1900(1900)
1900:2088.01
145.587
0
58032
11820.72672.89
00
0
2743.05
75.45
000
75.45
0
1057.21
0
0
0
723.749
HON
1184(1184)
1184:145.587
3554.78
789.7
00
0
4914.85
GMY
3.68882e+07(3.69e+07)
3.68909e+07:3.52454e+07
0
12638.6
0
789.7
73.25
ARG
93382.1(98297)
93382.1:0
0
9371.45
0
0
0
0
628.25
00
0
0
0
73.25
0
0
110014
71.6978
PAN
636(636)
636:5646.41
CUB
13424.9(15794)
13424.9:2765.08
4094.04
0 2708.57
9371.45
13076
0
0 0
789.7
0 019029.3
0 1067.33
0
099990.6
NZL
672.879(120750)
672.879:0
0
416989
CAN
1.63698e+06(2.32132e+06)
1.63698e+06:0
464265
0
1040080
JPN
2.92992e+06(2.92992e+06)
2.92992e+06:4.6024e+06
0
42.2
NIC
641.142(844)
641.142:1439.28
0
5646.41
HAI
1243.9(1509)
1243.9:2667.6
57.1508
239013
IRQ
5507.18(6851)
18135:0
6661470
42.2
1481.48
ITA
279558(493476)
291379:3.55954e+06
1343.82
12627.8
10912.8
0
19456.20
0
THI
21856(21856)
21856:32094.8
ETH
500(500)
500:10912.8
116066
0
34.0583 0
47.9111
0
149701
1.10738e+06
1.27466e+060
0
4.86026e+06
SAF
6054.42(290160)
6054.42:0
19860.2
2662.86
0
274101
0
42.2
1.57479e+06
0
9.13805 0
CHN
4987.32(244000)
4987.32:0
UKG
44863(1.35e+07)
91346.1:0
19248.8
23341.2
TUR
89004.2(108253)
112345:0
ROM
10213(10213)
10213:688358
EGP
17422.1(20085)
37282.4:0
15524.8
21844
2242.56
0
7447.37
58135.7
126298
0
409919
0
840027
RUS
38115.3(7.32416e+06)
65409.3:0
5633.28
0
POR
31988.6(39436)
90124.3:0
BUL
34517(34517)
34517:1.08244e+06
0
SWE
168686(187429)
168686:3704.58
URU
11936.8(12565)
11936.8:0
COS
953(953)
953:2708.57
SAL
1246.8(1465)
1246.8:4020.79
DOM
2113(2113)
2113:1067.33
AUL
9706.63(550072)
9706.63:0
A Visualization of the World in World War II
FRN
742009(742009)
742009:2.46676e+06
FIN
99871(99871)
99871:144320
MON
2400(3000)
2802.66:0
HUN
110555(110555)
110555:279836
SPN
93374(93374)
93374:107004
4.2
4 EMPIRICAL TESTING
0
267.35
0
100
267.35
0
267.35
100
0
25
0
0
25
0
0
0
296062
0
362353
39685.8
0
0
1358.95
0
0
0
0
4.89738e+06
0
0
90588.2
0
020412
0
218019
SWE
198234(198234)
198234:218019
0
CAN
3.55684e+06(3.84119e+06)
3.55684e+06:0
0 9921.45
0
342.55 552019
0
342.55
0
EGP
21568.1(26044)
63744.8:0
SPN
98408(98408)
98408:216251
0
43989.8
0
543251
396701 0
POR
40356.9(41230)
225295:0
89661.4
5435.8
04.93701e+06
0216251
6.70856e+06
0
0
150810
4.0047e+07
247.175
118920 0
1.50739e+07
254109
0
0
2.06494e+06
RUS
293615(7.9785e+06)
302506:0
0
1.74504e+06
4.38595e+06
0
IRN
20137.1(27179)
228719:0
THI
21856(21856)
21856:487289
599950
0
157562
186.775
BUL
34517(34517)
34517:2.76777e+06
0
0
1302.2
0
133538
MON
2813.22(3000)
160375:13137.6
0
0
SAF
94850.2(198429)
94850.2:0
090588.2
53971.5
0
0
0
0
5450.95
JPN
6.98987e+06(6.98987e+06)
6.98987e+06:1.29217e+07
ITA
412981(412981)
412981:1.6825e+07
GMY
4.48e+07(4.48e+07)
4.48e+07:4.97607e+07
0
81648
081648
0
3.31479
445.7
0
AUL
972173(1.81176e+06)
972173:0
NZL
224532(408240)
224532:0
0
ETH
446.685(500)
446.685:0
207
0
5450.950
BRA
98117.1(109019)
98117.1:0
0
TUR
64503.4(72406)
134584:0
1.46466e+060
USA
1.07411e+06(7.21e+07)
1.07411e+06:0
365690
10322
UKG
568004(1.54e+07)
591217:0
70080.37902.64
308101
0
ROM
10213(10213)
10213:2.56389e+06
184939873.104
0
435055
13137.6
342.55
8456.8
5648.2
42176.7
3173.7
0
148507
FIN
100407(100407)
100407:402616
7.03135e+06
0
230664
0
34294.4
179.966
1484460
58519.8
0
CHN
264357(331806)
264357:355368
FRN
742009(742009)
742009:7.26202e+06
IRQ
5643.38(6851)
39937.8:0
HUN
242120(242120)
242120:515067
A Visualization of the World in World War II
U
2000)
0:0
3455.7
0
65
347)
:0
)
AN
(4140)
33:0
COL
8468.3(8914)
8468.3:0
4.2
4 EMPIRICAL TESTING
4.2
A Visualization of the World in World War II
4.2.5
1944 - 1945
Figure 36: 1944 Europe
Figure 37: 1945 Europe
66
4 EMPIRICAL TESTING
4.2
A Visualization of the World in World War II
4 EMPIRICAL TESTING
1944 - 1945 was the end of the war. Japan began its last offensive in China, capturing
further territory in the south. In Europe, the Normandy landings make Germany unable to
counter-attack with the necessary speed and strength (Weinberg, 1994).
Table 13: 1944 Relation
Dyads in War
China - Japan
United Kingdom - France
United Kingdom - Japan
United Kingdom - Bulgaria
United Kingdom - Romania
Germany - Canada
Germany - Russia
Germany - Australia
Germany - New Zealand
Germany - South Africa
Germany - United Kingdom
Germany - Italy
Germany - Finland
Germany - Bulgaria
Hungary - Russia
United States - France
United States - Germany
United States - Japan
Russia - Hungary
Russia - Romania
Russia - Finland
Russia - Japan
Japan - South Africa
Japan - Australia
Japan - New Zealand
Italy - Bulgaria
Dyads in Militarized Conflict
Spain - Russia
United Kingdom - Hungary
United Kingdom - Finland
United Kingdom - Thailand
France - Hungary
France - Japan
Canada - Japan
Canada - Bulgaria
Thailand - Australia
United States - Hungary
United States - Bulgaria
United States - Romania
Germany - Iraq
Germany - Turkey
Germany - Portugal
Germany - Nicaragua
Germany - Hungary
Germany - Brazil
Germany - Iran
Germany - Colombia
Germany - Liberia
Germany - Romania
Germany - Sweden
Germany - Bulgaria
China - Russia
Romania - South Africa
Romania - Australia
Romania - New Zealand
Romania - Hungary
Russia - Bulgaria
Italy - Iraq
Italy - Bolivia
Bulgaria - Turkey
Japan - France
Japan - Brazil
Japan - Iraq
Japan - Liberia
Japan - Bolivia
Dyads in Alliance
United Kingdom - Egypt
United Kingdom - Russia
United Kingdom - Turkey
United Kingdom - Iraq
United Kingdom - Portugal
United Kingdom - Iran
Russia - Czechoslovakia
Russia - Mongolia
Russia - Iran
Russia - France
Japan - Thailand
Australia - New Zealand
In the New Year the Soviet army liberated the Auschwitz. They also continued its battles
from the east, while from the west the Allies raced with them to be the first to enter into
Berlin. The Russians reached Berlin first and Germany surrendered unconditionally on 7
67
4.2
A Visualization of the World in World War II
4 EMPIRICAL TESTING
May (Weinberg, 1994). The war in Europe was over.
In the Pacific, however, conflicts had continued to rage throughout this time. Plans were
being prepared for an Allied invasion of Japan, but fearful of fierce resistance and massive
casualties, the atomic bombs were dropped in Hiroshima and Nagasaki. The Japanese surrendered on 14 August. (Weinberg, 1994) The biggest conflict in history had lasted almost
six years and ended.
Table 14: 1945 Relation
Dyads in War
China - Japan
United Kingdom - France
United Kingdom - Japan
Germany - Canada
Germany - Russia
Germany - Australia
Germany - New Zealand
Germany - South Africa
Germany - United Kingdom
Germany - Italy
Germany - Finland
Germany - Bulgaria
Germany - France
Hungary - Russia
United States - Germany
United States - Japan
Russia - Japan
Japan - South Africa
Japan - Australia
Japan - New Zealand
Dyads in Militarized Conflict
Spain - Russia
United Kingdom - Hungary
United Kingdom - Thailand
France - Hungary
France - Japan
Canada - Japan
Thailand - Australia
United States - Hungary
Germany - Brazil
Germany - Iraq
Germany - Portugal
Germany - Hungary
Germany - Peru
Germany - Uruguay
Germany - Argentina
Germany - Egypt
Germany - Venezuela
Germany - Paraguay
Germany - Romania
Russia - Iran
Russia - Turkey
Russia - Japan
China - Russia
Italy - Iraq
Japan- Venezuela
Japan - Paraguay
Japan - Iran
Japan - Egypt
Japan - Chile
Japan - Argentina
Japan - Uruguay
Japan - Peru
Japan - Mongolia
Japan - Brazil
Japan - Iraq
Japan - Liberia
Japan - Bolivia
68
Dyads in Alliance
United Kingdom - Egypt
United Kingdom - Russia
United Kingdom - Turkey
United Kingdom - Iraq
United Kingdom - Portugal
United Kingdom - Iran
Russia - Czechoslovakia
Russia - Mongolia
Russia - Iran
Russia - France
Russia - China
Russia - Poland
Russia - Yugoslavia
Japan - Thailand
Australia - New Zealand
69
0
87765.9
Figure 38: 1944 Europe
0
0
4.89321e+07
0
04428.65
00
0
351064
HUN
433638(433638)
433638:1.66033e+06
403402
0
USA
221201(8.7e+07)
221201:0
1.13624e+06
0
0
4428.65
ROM
10213(10213)
10213:3.17633e+06
45.450
10492.2
0
AUL
877659(1.75532e+06)
877659:0
0
617.1
0
0
0
827.21
0
28.45
0
0
0
351064
0
1.05062e+06
0
0
028.45
342.55 0
0
1.75932e+06
BUL
34517(34517)
34517:2.09103e+06
0
0
40300
724462
0
0
7200
0
0
18460600
1.79799e+07
0
29439.82439.74
2822.52
2646.39
0
35792.9
22911.8
0
131926
SPN
102563(102563)
102563:131926
0
23359.4
0
308583
619779
0
5156
31627.9
0
167.446
615.177
1.3876e+06
1.61891e+06
0
0
0
0
90108.4
0
0
00
71194.6
70420.2
FRN
1.21408e+06(1.21408e+06)
2.833e+06:1.85997e+07
253491
0
0
0
112526
EGP
26126.8(26742)
26294.3:0
NZL
281682(495720)
281682:0
POR
36322(43661)
67949.9:0
1955.82
321.3480
CAN
2.69337e+06(3.62231e+06)
2.69337e+06:0
17110.9342.55
181115
0
JPN
1.72e+07(1.72e+07)
1.72e+07:2.42459e+07
4.02619e+060
0
0
UKG
106730(1.63e+07)
139107:0
0
19721.6
099144
THI
21856(21856)
21856:107488
RUS
57961.8(8.09456e+06)
96794.5:0
2183.05
32521.4 1048.21 025782.2
0
2.83495e+06
8.05321e+06
0
24786
7200
MON
2400(3000)
20860:0
206304
IRQ
4775.14(6851)
37296.6:16768.4
IRN
24194.8(30822)
56457.1:0
0
591318
0
277814
0
1541.1
0
1.80494e+07
0
1.33539e+06
0
342.55
GMY
5.07e+07(5.07e+07)
5.07e+07:6.13707e+07
0
40300
0 87765.9
SAF
120073(201500)
120073:0
BRA
129600(144000)
129600:0
FIN
105498(105498)
105498:323911
CHN
81099.9(195582)
81099.9:69238.8
ITA
7963.85(342218)
7963.85:0
8238.76
0
BOL
5347(5347)
5347:8238.76
A Visualization of the World in World War II
NIC
863.55(909)
863.55:0
TUR
79715.7(88573)
79715.7:0
SWE
199351(209843)
199351:0
COL
11724.9(12342)
11724.9:0
LIB
512.1(569)
512.1:0
4.2
4 EMPIRICAL TESTING
0
1.00362e+06
0
0
135320
0
239976
30059.3
HUN
433638(433638)
433638:2.88005e+06
451168
0
5900.84
2952.86
00
0
2.50037e+07
CZE
244542(305677)
251629:0
99806.10
61135.4
7087.07
RUS
319056(8.58908e+06)
623188:0
4.1377e+06
0
67.6664
8842.78
MON
2932.33(3000)
11775.1:0
21813.8
0
1.28299e+06 0
5631.26
80.1921
IRQ
6021.87(6851)
155634:14928.1
00
0
34052.7
149613
176.305
9204.6
11279
62.9039
0
0 1.17332e+06
0
0
2.11091e+06
0
00
1.48907e+06
USA
251653(9e+07)
251653:0
0
0
1541.1
0
3.14562e+07
0
POR
34517.2(46023)
45796.3:0
3.48641e+06
0
452833
0
1208660
JPN
4.00248e+06(4.00248e+06)
4.00248e+06:3.75862e+07
0
0
BOL
5347(5347)
5347:13222.7
0
2.34639e+06
4.29688e+060
57886.1
0
UKG
1.18338e+06(1.7e+07)
1.22782e+06:0
2.24981e+06
0
1790710
IRN
26247.8(30822)
37780:0
15270.6
342.55
4919.6
6634.42
EGP
19678.4(24598)
26312.8:0
0
13222.7
0247.37
2301.15
0
BUL
34517(34517)
34517:5.82524e+06
2.62992e+06
0
0
0
0
NZL
319936(429590)
319936:0
1332180
0
39958.4
GMY
1.06e+07(1.06e+07)
1.06e+07:3.33258e+07
0207348
AUL
831656(1.48429e+06)
831656:0
133218
0
8559
0
19833.9
TUR
374081(396678)
374081:0
2.74387e+07
21479.5
0
00
0
0
0
74214.6
0
28.450
0
29172.7
9863.38 0
74214.6
48215.9
2763.32
0
0
296858
ROM
10213(10213)
10213:3.22078e+06
58129.4
00
THI
21856(21856)
21856:195081
41307.4 0
SAF
126193(206537)
126193:0
10815.7
0
532873
0
85590
0
28.45
SWE
205498(216314)
205498:0
CAN
1.86506e+06(2.66436e+06)
1.86506e+06:0
BRA
154062(171180)
154062:0
LIB
512.1(569)
512.1:0
A Visualization of the World in World War II
FIN
105978(105978)
105978:1.10343e+06
0
1.71782e+06
73449.4
2286.12
70
SPN
119722(119722)
119722:135320
FRN
1.23051e+06(1.23051e+06)
2.94832e+06:2.91414e+07
CHN
204512(228612)
204512:71163.3
ITA
160903(305412)
160903:0
4.2
4 EMPIRICAL TESTING
4.2
A Visualization of the World in World War II
4.2.6
4 EMPIRICAL TESTING
Simulation Results
Table 8 shows the probability of being in different states for selected countries in World
War II. Italy and France were not included because the former withdrew from the war in
1943 and the latter was conquered and turned into Vichy France from 1942 onwards.
Table 15: Probability of Being in Different States for Selected Countries from 1939-1945
Country-Year
Germany-1939
Germany-1940
Germany-1941
Germany-1942
Germany-1943
Germany-1944
Germany-1945
Japan-1939
Japan-1940
Japan-1941
Japan-1942
Japan-1943
Japan-1944
Japan-1945
UK-1939
UK-1940
UK-1941
UK-1942
UK-1943
UK-1944
UK-1945
Soviet Union-1939
Soviet Union-1940
Soviet Union-1941
Soviet Union-1942
Soviet Union-1943
Soviet Union-1944
Soviet Union-1945
Pr(Vulnerable)
0.08%
0%
0%
72.15%
99.94%
100%
100%
0%
0%
0%
100%
100%
100%
100%
1.17%
99.96%
99.68%
0.04%
0%
0%
0%
0.05%
0%
100%
0.7%
0.01%
0.02%
0%
Pr(Defensive)
99.92%
100%
2.52%
27.85%
0.06%
0%
0%
100%
0.07%
2.52%
0%
100%
0%
0%
98.83%
0.04%
0.32%
29.38%
0.08%
0%
0%
99.95%
100%
0%
27.15%
0.06%
99.49%
99.81%
Pr(Powerful)
0%
0%
97.48%
0%
0%
0%
0%
0%
99.93%
97.48%
0%
0%
0%
0%
0%
0%
0%
70.58%
99.92%
100%
100%
0%
0%
0%
72.15%
99.93%
0.49%
0.09%
The simulation results indicate the year of 1942 as the watershed of the war, during which
the greater involvement of the US profoundly reversed the fortunes of the Axis powers. They
also show the processes within which the Axis powers turned into a powerful alliance from
a defensive alliance, and eventually became vulnerable, and the the Allies lifted itself from
vulnerability to a powerful alliance
71
5
5
EXTENDING THE MODEL
Extending the Model
In all, the paper makes two main contributions: first, for the first time, it has provided
basic and necessary theorizing of military alliances with graphic-theoretic concepts and network games, having laid a solid microfoundation for understanding the workings of military
alliances. Its theoretical implications go beyond military alliances and can be extended to
alliances in general; second, the theoretical predictions of the game rely heavily on empirical
evidence from 1816 to 2012. The model can be applied to any interstate conflict involving
military alliances. I discussed specifically the cases of World War I and World War II and
have proven that the model is even robust to cases of such complexity. The simplicity of
the model has enabled the introduction of the basic ideas and intuitions and yielded clear
results.
The model presented here is a simple one, leaving room for further extensions, in particular for the sake of applications in studying more complex situations. Most obviously, a
major extension would be to incorporate alliance formation and stability into the current
model. It is straightforward and natural to model agents’ establishment of new relations as
well as deviations from current relations under the current framework. Some previous work
on the evolution of social and economic networks(Jackson and Watts, 2002; Jackson and
Zenou, 2012) can be partly combined with the current baseline model for this aim.
There are several directions in which formation and stability of military alliances could
be studied, which I intend to follow up. One possibility would be to introduce a novel but
intuitive relation formation and deviation protocol into the current model, which is based
on countries’ trade-off between the costs and benefits of doing so. Since my model uses
directed graph, it would be necessary to assume that relation formation should be bilateral
and relation deviation be unilateral in terms of ally and the reverse in terms of foe. Another
possible direction would be to study different initial states of relation structures and their
effects on the final structures in equilibrium as a result of countries’ optimizing behavior.
This might overcome another simplification of the model.
72
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76
A APPENDIX
A
Appendix
List of Figures and Tables
Figures
1. Figure 15 Geopolitical Map of Europe in 1914
2. Figure 16 Geopolitical Map of Europe in 1915
3. Figure 19 Geopolitical Map of Europe in 1916
4. Figure 21 Geopolitical Map of Europe in 1917
5. Figure 22 Geopolitical Map of Europe in 1918
6. Figure 26 Geopolitical Map of Europe in 1939
7. Figure 28 Geopolitical Map of Europe in 1940
8. Figure 30 Geopolitical Map of Europe in 1941
9. Figure 32 Geopolitical Map of Europe in 1942
10. Figure 33 Geopolitical Map of Europe in 1943
11. Figure 36 Geopolitical Map of Europe in 1944
12. Figure 37 Geopolitical Map of Europe in 1945
13. Figure 17 Game Solution for Europe in 1914
14. Figure 18 Game Solution for Europe in 1915
15. Figure 20 Game Solution for Europe in 1916
16. Figure 23 Game Solution for Europe in 1917
17. Figure 24 Game Solution for Europe in 1918(Without US Entry)
18. Figure 25 Game Solution for Europe in 1918(With US Entry)
19. Figure 27 Game Solution for Europe in 1939
20. Figure 29 Game Solution for Europe in 1940
21. Figure 31 Game Solution for Europe in 1941
77
A APPENDIX
22. Figure 34 Game Solution for Europe in 1942
23. Figure 35 Game Solution for Europe in 1943
24. Figure 38 Game Solution for Europe in 1944
25. Figure 38 Game Solution for Europe in 1945
Tables
1. Table 1 Table of Notations
2. Table 2 Relation Patterns of Europe in 1914
3. Table 3 Relation Patterns of Europe in 1915
4. Table 4 Relation Patterns of Europe in 1916
5. Table 5 Relation Patterns of Europe in 1917
6. Table 6 Relation Patterns of Europe in 1918
7. Table 7 Simulation Results for Selected European Countries in WWI
8. Table 8 Relation Patterns of the World in 1939
9. Table 9 Relation Patterns of the World in 1940
10. Table 10 Relation Patterns of the World in 1941
11. Table 11 Relation Patterns of the World in 1942
12. Table 12 Relation Patterns of the World in 1943
13. Table 13 Relation Patterns of the World in 1944
14. Table 14 Relation Patterns of the World in 1945
15. Table 15 Simulation Results for Selected Countries in WWII
78
A APPENDIX
Data Appendix
Sources
1. Country Total Capacity: National Material Capabilities Dataset (v4.0) in Correlates
Of War Project
2. War and Militarized Conflict: Militarized Interstate Dispute Dataset in Correlates Of
War Project
3. Alliance Membership: The Alliance Treaty Obligations and Provisions (ATOP) Dataset
Coverage
Table 16: Countries Included in Empirical Analysis
Country
Abbre.
Country
Abbre.
Afghanistan
AFG
Iran
IRN
Argentina
ARG
Iraq
IRA
Austria-Hungary
AUH
Ireland
IRE
Austria
AUS
Japan
JPN
Australia
AUL
Latvia
LAT
Albania
ALB
Liberia
LIB
Belgium
BEL
Lithuania
LIT
Bolivia
BOL
Luxemburg
LUX
Brazil
BRA
Mongolia
MON
Bulgaria
BUL
New Zealand
NEZ
Canada
CAN
Nicaragua
NIC
Chile
CHI
Norway
NOR
China
CHN
Panama
PAN
Colombia
COL
Paraguay
PAR
Costa Rica
COS
Peru
PER
Cuba
CUB
Poland
POL
Czechslovakia
CZE
Portugal
POR
79
A APPENDIX
Table 16: (continued)
Country
Abbre.
Country
Abbre.
Denmark
DEN
Russia or the Soviet Union
RUS
Dominica
DOM
Romania
ROM
Ecuador
ECU
Saudi Arabia
SAU
Egypt
EGY
South Africa
SAF
El Salvador
SAL
Spain
SPN
Estonia
EST
Sweden
SWE
Ethiopia
ETH
Switzerland
SWI
France
FRN
Thailand
THI
Finland
FIN
Turkey or the Ottoman Empire
TUR
Germany
GMY
The Netherlands
NTH
Greece
GRC
United Kingdom
UKG
Guatemala
GUA
United States
USA
Haiti
HAI
Uruguay
URU
Hungary
HUN
Venezuela
VEN
Honduras
HON
Yugoslavia
YUG
Italy
ITA
80