CESifo, a Munich-based, globe-spanning economic research and policy advice institution
Venice Summer Institute 2014
Venice Summer Institute
July 2014
BEHAVIOURAL POLITICAL ECONOMY
Organisers: Heinrich Ursprung, Urs Fischbacher and Arye Hillman
Workshop to be held on 21 – 22 July 2014 on the island of San Servolo in the Bay of Venice, Italy
CHOOSING A FUTURE BASED ON THE PAST:
INSTITUTIONS, BEHAVIOR, AND PATH
DEPENDENCE
Jenna Bednar, Andrea Jones-Rooy and Scott E. Page
CESifo GmbH • Poschingerstr. 5 • 81679 Munich, Germany
Tel.: +49 (0) 89 92 24 - 1410 • Fax: +49 (0) 89 92 24 - 1409
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Choosing a Future based on the Past: Institutions,
Behavior, and Path Dependence
(DRAFT)
Jenna Bednar, Andrea Jones-Rooy, and Scott E Page∗
University of Michigan
July 14, 2014
Abstract
In this paper, we link institutional features to individuals’ behavioral repertoires and
then connect those behaviors to optimal choices over future institutional choices. In our
framework, institutions create incentives that advantage some behaviors over others. Those
behaviors become part of the context for future institutions creating spillovers between institutions. These spillovers result in path dependent behaviors and outcomes. They also
imply path dependence in the institutional choice, as some subsequent institutions will better leverage existing behaviors than others. We also find that institutions vary in the extent
to which they create adaptive behavioral repertoires that reduce path dependence allowing
for greater flexibility in future choices.
∗
You can contact us at [email protected] or [email protected]. We thank Anna Grzymala-Busse, Bill
Zimmerman and Gerry Mackie for helpful conversations, and seminar participants at ICER (Turin) and
APSA, especially our discussants Daniel Diermeier and Tasos Kalandrakis. For research assistance, we are
indebted to Jennifer Miller and Neill Mohammad. Funds to support this research project were provided by
the McDonnell Foundation, an NSF IGERT grant, and AFOSR-MURI Grant 57100001867 and AOR Grant
need NUMBER
1
Introduction
Individuals interact in multiple contexts ranging from formal political and economic institutions to informal organizational and social settings. Ideally, those interactions produce
efficient, fair outcomes, but often they do not. Institutional failure can result from poor design. To borrow the language of mechanism design: the institution may not implement the
social objective. Failure can also arise because the people interacting within the institution
do not act as expected.
This second sort of failure underpins this paper. We ask why people behave as they do
within institutions. One approach would be to assume that human behavior differs from the
rational choice models assumed by most formal models in social science and to embrace the
behavioral economic approach. To do so would be to replace homo economicus with actors
who better resemble real humans with all of their cognitive biases and computational limits.
Two empirical regularities limit the generality of this approach. First, evidence suggests
that behavior and institutional performance often depend on context. How people behave
varies by culture even for simple games. Experiments in which people form different cultures
play identical games reveal diverse outcomes. For example, Roth et. al. (1991) find that
players from three countries behave differently in bargaining games, and they attribute the
variation in play to cultural differences. A study by Henrich et al. (2004) reveals that
individuals in different cultures play the Ultimatum Game very differently. In addition, a
study, which also covers fifteen distinct populations even finds differences in how people
play simpler dictator game (Henrich et al 2010). The authors of that study conclude that
prosocial behavior is not solely the product of an innate psychology, but also reflects norms
and institutions that have emerged over the course of human history. Finally, some have
argued that many if not most of the documented biases have only been shown in Western
societies, so many think of as human biases, may be Western biases (Medin and Chandler
2010).
Second, decades of research in experimental economics, political science, and sociology
2
demonstrates unequivocally that people learn (Fudenberg and Tirole 1998, Camerer 2003,
Morton and Williams 2010). Learning tends to lead to equilibrium, though not necessarily
to efficient equilibria.
In this paper, we advance a possible contributing explanation for both variations in institutional performance and the the fact that people learn: behavioral spillovers. These
spillovers influence what behaviors individual learn to play and as result influence the effectiveness of particular institutional forms. Pushing the logic one step forward, it follows
then that different communities may choose different types of institutions to perform similar
tasks, which implies a degree of institutional path dependence (Pierson 2000, Page 2006).
We construct a framework in which we represent institutions as game forms. When placed
in an institutional context, individuals learn to play the game using a standard learning
rule. Our framework builds from game theoretic models of institutions (Diermeier and
Krehbiel 2003) in that we characterize institutions as game forms, and we assume purposeful
individuals. However, our approach differs in that we assume that context matters and that
the performance of an institution depends on the existing set of behavioral rules. Thus, we
our approach bridges the gap between stark game theoretic models and thicker descriptive
accounts of institutions.
Spillovers occur because when confronted with a new institutions, individuals initially dig
into their behavioral repertoires and use a behavior that has worked for them in a similar
game. They don’t stick to that behavior necessarily. It merely serves as an initial behavior
from which they attempt to learn something that produces a better outcome. As we shall
show, these initial predispositions can have rather large effects and unexpected effects.
Intuitively, one might think that if agents learn to cooperate, be selfish, or alternate in
one game that those outcomes would then be more likely in subsequent games, and in fact,
we find that to be to a large extent true. But not all spillovers are as obvious. For example,
we will find that learning to alternate can lead to more selfish behavior in a Stag Hunt game
than can learning to be Selfish. This unexpected result can only be understood by looking
deeply into behaviors as we shall do in the paper.
3
This result and others shed light on why institutional performance varies so widely across
cultures and contexts and why people from different places play identical games differently
The reason: Institutions produce behaviors and those behaviors become part of individual’s
behavioral repertoires. They become rules of thumb that people follow at least initially.
Though the framework we present considers only two by two games, we intend for the
results to be interpreted more broadly as an extension of standard game theoretic models of
institutions in political science and economics. To make that point requires first providing
some background. The institutions as games idea originated in the field of mechanism
design (Reiter 1986). Mechanism design characterizes institutions as action sets, payoffs,
and communication structures. Optimal institutions align individual incentives with the
collective interests and aggregate privately held information to the extent possible given
constraints on participation and misrepresentation. In brief, institutions create incentives
to advantage some behaviors over others and for the revelation of information of collective
value or interest. Mechanisms are then evaluated by their ability to produce good outcomes
in equilibrium (Diermeier and Krehbiel 2003). Owing to this focus on outcomes, nearly the
entire mechanism design literature considers single institutions.1
Here, we extend that standard model by considering multiple institutions added sequentially. Were the performance of each of these institutions independent of previous institutional choices, then each could be considered in isolation and neither the past nor the present
would hold sway over the future.
But the evidence mentioned above suggests that context does matter. Individuals do
not confront a new institution with a clean slate. Instead, they’re burdened by past beliefs
and behaviors. Past behaviors can influence institutional performance in two ways. First, a
current behavior might be an equilibrium behavior in the new institution, which we model
as a game. But that equilibrium may or may not be efficient. However, it will be what
the agents do. In this case, behavior can be thought of as an equilibrium selection device.
Although in the culture as equilibrium selector literature, beliefs and not behavior are the
1
See Page (2012) for a survey and critique of mechanism design along the lines implicit in this paper.
4
mechanism that selects the equilibrium.
Second, and this is the primary focus of this paper, an existing behaviors may fail to be
an equilibrium behavior in the new institution. However, it may be a good starting point,
an initial behavior. And, if final learned behavior depends on initial behaviors, then past
behaviors can influence current behaviors.2
The notion of applying existing strategies or actions in a new context has strong support
(see Gilboa and Schmeidler (1995) for a survey). For example, if individuals learn how to
cooperate in one setting, they may also begin by cooperating in another setting.3 Recent
experimental research demonstrates that these behavioral spillovers exist in laboratory setting (Bednar, Chen, et al 2011, 2012). In addition, empirical evidence supports the claim
that human intelligence arises from the interaction between our mental models of the world,
stores of physical behaviors we might use to respond to the world, and the dynamic world
itself (Clark 1997). Thus, we can think of people as having linked cognitive and physical
subroutines: individuals carry around with them a collection of “tools” in the form of learned
behaviors that they invoke selectively as they confront new challenges and opportunities.4
These learned behaviors are often consistent within an individual and coordinated across
individuals (Bednar, Bramson, Jones-Rooy, and Page 2010).
In our model, we characterize the process of adaptation as a dynamic system with three
parts: (i) a representation of strategies, (ii) the initial strategies (often a distribution over
them), and (iii) a learning rule for creating new strategies. The behaviors that the individuals in our model learn will nearly always be equilibria of the games they play. Research has
shown that citizens use rules of thumb when they make inferences about new political can2
To explicitly represent individuals’ behaviors, we rely on automata (Rubinstein 1986, Kalai and Stanford
1988, Miller 1996).
3
Differences in how members of a community learn could also affect institutional performance. One
community may be more individualistic, another may be more collectively minded (Inglehart 1977) Individual
learning rules and collective learning rules differ in the equilibria they locate (Golman and Page 2010). Thus,
societies that learn differently can experience different outcomes from the same institution. Though variation
in learning rules can produce distinct equilibria in different communities, it would not, on its own, produce
path dependent institutional performance.
4
These physical behaviors may resemble tacit knowledge in that they may be inaccessible to the conscious
mind (Polanyi 1974).
5
didates(Mondak and McCurley 1994, Ottati 1990, Brent and Granberg 1982). On deriving
opinions about which candidate to support, Brady and Sniderman (1983) find that the most
common heuristic used by Americans is what they call the “likability heuristic” – that is,
Americans give much more weight to how much they personally like each candidate than to
other characteristics like policy positions or background when making choices about whom
to support. Relatedly, legal research has shown that jurors also simple heuristics to weigh
evidence in a trial (Saks and Kidd 1981). In economics and psychology, numerous studies
show that people rely on cognitive “shortcuts” both in decision contexts and in strategic setting (see Kahneman and Tversky 1979, Camerer 2003). Heuristics can be time- and energysaving and produce nearly optimal actions (Gigerenzer and Selten 2002, Clark 1997, Barber
1977). For example, Simpson (2004) finds that cooperation is ubiquitous in a community
of citizens who apply prosocial heuristics to social dilemma games, such as the Prisoner’s
Dilemma.
Our focus in on how these behaviors depend on institutions. We find strong evidence that
both the set of existing institutions as well as can the order in which they arise can influence
behaviors. We also find that the optimal institutional choice for a community depends on
the set of previous institutions and on the order the institutions were put in place. These
last two results imply that the best institutional choice cannot be made without regard to
existing institutions. Therefore, the model provides a candidate explanation for institutional
path dependence without explicitly assuming increasing returns or positive feedback (Pierson
2000, 2004, Page 2006). Finally, we show the some early institutional choices create more
flexibility than others. Specifically, we find that some institutions dramatically limit future
choices over institutions.
One can place the behavioral repertoires that emerge in our model comprise a part
of what political scientists and anthropologists with the larger category of culture. The
influence of culture on institutional and organizational outcomes has been the subject of
substantial ethnographic and case study research (Platteau 2000). On a range of policy
problems, such as environmental protection, state formation, and economic development:
6
it is well documented that one-size-fits-all solutions often don’t work (Ostrom 2007) and
sometimes fail miserably (Stiglitz 2003, Easterly 2001, Svensson and Dollar 1998). More to
the point, wholesale copying of institutions that have worked elsewhere rarely works (Fish
1995).5 The failure of the Washington Consensus policies to deliver economic growth in
developing countries in the ’90s is representative of this larger point. Some countries, such
as Botswana in recent years, have responded well to World Bank and IMF interventions
and exhibited rapid growth, while others, such as Zambia, have seen few results – even
negative growth (Irving 1998). Our findings align with that intuition, and they suggest that
institutions should be designed with an eye toward leveraging existing behaviors. Institutions
that build off existing behaviors should perform better than those that demand wholesale
changes. Anecdotal evidence supports this view. Efforts by the Chinese Government in the
early 1950s to implement gender equality in rural households that proved most enduring
were those that validated existing divisions of labor (Hershatter 2002, p. 57). On the other
hand, laws implemented that ban arranged marriage and bride-buying in rural China have
not translated into better treatment of women (Allen 2006).
A Model of Sequential Institutions and Behavioral Spillovers
In the model, agents confront a sequence of institutions that we formalize as games. Each
game is played repeatedly. The agents first learn to play the initial game in this sequence
They then add a second game, and eventually a third. The spillovers arise because the
agents initial strategies in that second game depend on the strategies that they learned in
the first game. The extent of that dependence, we refer to as the behavioral spillover. In the
most extreme case, every agent initially plays the new game using the strategy it learned in
the first game. The agents then learn how to play in this second game. This construction
produces avertical ensemble of games in which the learned behaviors in the second game
5
The evidence that behavioral patterns, and more broadly, that culture matters can be seen in other data
as well. Evidence suggests that adherence to past behaviors despite new incentives can span generations.
For example, in the United States, the number of offspring in immigrant families lies between the average
number in their home culture and the U.S. average (Fernandez and Fogli 2005).
7
can depend on the strategies used in the first game. This differs from a situation in which
the agents confront the entire ensemble of games at the same time, or a horizontal context
(Bednar and Page 2006).6
This vertical influence on behavior and therefore outcomes creates the possibility of both
set and path dependent behaviors. The former would hold if the learned behavior in the
second game depends on the first game. The latter would be true if the same two games
played in a the opposite order produce different behaviors. If either set of path dependence
arises, then it also follows that the optimal choice of a game form could be a function of the
set or path of previous choices. Therefore, in addition to behavioral dependence (the notion
that behaviors depend on the set or order of earlier games), there may also exist what we
call institutional dependence in that the optimal choice of an institution, i.e. game form,
may depend on the set or order of previous games.
It is of course possible that the learned behavior in the second game does not depend in
any way on the strategies developed in the first game. If so, then we will say that the second
game is immune to behavioral spillovers. We will find that games with dominant, pareto
efficient strategies are immune, but that games that have multiple equilibria in the repeated
game setting, tend not to be immune.
Set and Path Dependence
To lay the groundwork for our formal model, we present examples of set and path dependence.
These examples demonstrates how behavior can bleed from one game to the next. We begin
with an example of set dependence. In this example, the second game will be what we call
the Knife Edge Game.
6
Ensembles of games differ from nested games in which one action has implications in many games
(Tsebelis 1991).
8
Knife Edge Game
Row
Column
C
S
C 8,8 2,14
S 14,2 4,4
The repeated version of the Knife Edge game has many equilibria. Here, we focus on two
of those equilibria: the Cooperative equilibrium, in which both agents choose C in each
period, and the alternating equilibrium, in which the agents alternate between the outcomes
(S, C) and (C, S). In each of the first two equilibria, each agent receives an average payoff
of eight.7
Recall that the Knife Edge game is played second. We want to see if behavior in that
game depends on the first game. Let’s suppose that the agents first play Prisoners’ Dilemma
game. In this game, the agents may well learn to cooperate.
Prisoners’ Dilemma Game
Row
Column
C
S
C 8,8
1,10
S 10,1
2,2
Assume a maximal level of the behavioral spillover, so that when the Knife Edge Game is
added, the agents initially play the cooperative strategy that they were using in the Prisoners’
Dilemma. This might be Tit for Tat, or it might be Grim Trigger. The agents then learn.
The strategy used in the Prisoners’ Dilemma might become intrenched in the second game.
The agents might learn to play the cooperative equilibrium in the Knife Edge game as well.
If so, we will say that the learned behavior in the first game spills over into the second game.
Suppose that instead, the first game played was what we call the Alternation Game.
In this game, the efficient equilibrium strategy calls for each pair of agents to alternative
between (C, S) and (S, C). We refer to this as the alternation strategy. If the agents initially
play the alternation strategy, then even after learning, they may stick with this strategy.
7
Note that we assume no discounting.
9
Alternation Game
Row
Column
C
S
C 2,2 -2,10
S 10,-2 2,2
The table below shows how learned behavior in the initial game can influence the learned
behavior in the second game through the spillover.
Ensemble Composition affects Behavior
Game 1
Behavior
Game 2
Behavior
Community 1
Community 2
Prisoners’ Dilemma Alternation
(Cooperate)
(Alternate)
Knife Edge
Knife Edge
(Cooperate)
(Alternate)
In this example, behavior differs in the Knife Edge game across the two communities because
the initial games differ and those initial games produce behaviors that then get applied in
the Knife Edge game. As this example suggests, we are using the learning rules as a type
of refinement criterion. By the Folk Theorem, any repeated game has lots of equilibria.
We’re using an evolutionary learning rule to select from among those equilibria. The initial
conditions for the rules are influenced by the existing set of games.
To show path dependence, we must show that the behaviors depend on the order in which
the games are played. To see how this could occur, assume that in one sequence the Knife
Edge game is played first and the Alternation Game is then added. Suppose that in both
games, individual learn to play cooperatively, i.e. to take the action pair (C, C). Assume
next that we switch the order so that the Alternation Game is played first. Now, suppose
that the individuals learn to alternate in the first game and then use the same strategy in
the second game. Thus, the same games, in different orders, produce different behaviors.
10
Path Dependent Behavior
Game 1
Behavior
Game 2
Behavior
Sequence 1 Sequence 2
Knife Edge Alternation
(Cooperate) (Alternate)
Alternation Knife Edge
(Cooperate) (Alternate)
Though we have only considered two games so far, we could add a third game. When
adding a third game, we must make some sort of assumption about how initial behavior
depends on the past behavior. If the agents use the same strategy in each of the first two
games, then we can assume that they use that strategy initially in the third game. If the
strategies differ, then we can assume that the agents are more likely to use the strategy of
the game that’s more similar to the new game. In this case, that would be the Knife Edge
game.
If we assume that all agents cooperate in both games in the first sequence, they we might
well expect cooperation in the the Prisoners’ Dilemma. IF the players alternate in each of
the first two games, then it’s less clear what the agents will learn to play in the Prisoners’
Dilemma. They could alternate. They could cooperate. Or, they could defect.
The Model
We now present our formal model. We assume a finite population of agents who interact
in multiple institutional contexts that we model as repeated games. New institutions are
added sequentially. Agents first play one game, and then a second game is added. Agents
learn to play each new game, until another game is added. Therefore, each period in which
a new game is introduced consists of numerous iterations each containing multiple rounds of
play giving agents have the opportunity to learn effective behaviors in the new institution
before another institution is added.
Within this general framework, the game forms could include any number of actions
or strategies and involve any number of players. Here, we restrict attention to seven two
player game forms. Each game has two actions, one that is more selfish (S) and one that is
11
more cooperative (C). In this way, it makes sense to think of agents transferring behaviors
from one game to another. We have already described three of the games: the Knife Edge,
Alternation and Prisoners’ Dillemma games. The fourth game is the familiar Stag Hunt
game in which the selfish strategy has a guaranteed payoff, but cooperation gives a higher
payoff only if the other player cooperates as well. The fifth game, we call the Self Interest
game. In this game, choosing to be selfish is a strictly dominant strategy.
Self Interest (SI)
Row
Stag Hunt (SH)
Column
C
S
C 0,0 0,6
S 6,0 8,8
Row
Column
C
S
C 8,8 0,6
S 6,0 6,6
The final two games are asymmetric, advantaging either the row or column player. Each
also has two pure strategy equilibria in which one player cooperates and the other plays
selfishly. We refer to these as Top Right and Bottom Left. The games are meant to represent
institutions in which particular roles (represented as being the row or column player) are
endowed with advantages. These games can be thought of as capturing contexts in which
an agent in a particular role, say manager, or with a higher status, has an advantage. One
question that we will consider is whether behaviors that advantage one player spread to later
games which are not symmetric.8
Top Right Game (TR)
Row
C
S
Bottom Left Game (BL)
Column
C
S
4,6
6,10
8,2
4,6
Row
C
S
Column
C
S
6,4
2,8
10,6
6,4
Note that all six games have a maximal joint payoff of sixteen. We will denote the
8
Note all of these games with the exception of Stag Hunt are analyzed in Bednar and Page (2007).
12
efficiency of the outcomes at the end of the learning process as the average total payoff
divided by sixteen.
We capture the strategies of the agents using finite state automata that can encode common repeated game strategies such as tit for tat, grim trigger, alternate, and always defect. In
games such as those we consider here, they have proven capable of generating outcomes that
qualitatively align with what people produce in laboratory experiments (Rubinstein 1986,
Kalai and Stanford 1988, Miller 1996). The use of the automaton allows us to effectively
take snapshots of the agent’s behavioral rules.
Our specific formulation assumes that for each game, each agent uses an automata that
consists of six binary variables known as bits. When playing a game, an agent is designated
as either the row player of the column player. Two of the bits denote the agent’s initial
action, either C or S, if the agent is the row player and the initial action if the agent is
the column player. The other four bits denote the agent’s action as a function of the its
action and its opponent’s action in the previous period. There are four such possible pairs:
CC, CS, SC, SS.
The strategy of agent i in game G Θi (G) can be written a follows:
{Row 1st Action, Column 1st Action, Action(CC), Action (CS), Action(SC), Action(SS)}
where Action(CC) denotes the action following the outcome CC
To provide some intuition for this representation of strategies, the later two pairs of bits
bits can also be thought of as capturing behavior in two mental states: a cooperative state
and a selfish state. Given how we represent strategies, the third and fourth bits describe
how the agent will behave in the next period following a cooperative action by the other
agent. If the third and fourth bit are set to C, this means that once the agent cooperates,
it will cooperate forever. The fifth and sixth bits represent the selfish mental state. If the
agent’s fifth bit equals C and its sixth bit equals S, then following a selfish action, the
agent will copy the behavior of it’s opponent. Later, we will characterize this particular
behavior as matching. Note that there exist sixty-four unique automata and that each
13
encodes a reasonable strategy. For example, Tit for Tat is represented as {C, C, C, S, C, S},
Grim Trigger is represented as {C, C, C, S, S, S}, and Win Stay, Lose Shift, is represented as
{C, C, C, S, S, C}.
Evolving Strategies
We assume a population of sixty-four agents.9 . We arrange the agents in a circle and assume
that each agent plays both as row and column player against the two agents to its left and the
two agents to its right. Each interaction lasts forty rounds. Having agents play in a network
increases the likelihood that cooperative and alternating strategies will emerge. Agents learn
new strategies through mimicry and random search.
Mimicry After each iteration of twenty-five rounds, each agent copies the automata with
the highest total payoff from among its four opponents and itself.
Random Search After each iteration, with a small probability, each bit in each agent’s
automaton gets randomly assigned with probability 0.02.
We assume that agents conduct both mimicry and random search for one hundred iterations. We then turn off random search for fifty periods so as to allow for more convergence
on common best strategies.
Results
We first presenting outcomes for the seven individual games assuming a uniform initial
distribution over strategies.. These results provide a baseline from which we can identify
set ad path dependent outcomes and behaviors. We classify outcomes as cooperative, selfish,
diagonal: alternating, or diagonal: asymmetric using the following procedure. We first sum
the percentage of outcomes in which the two agents took different actions. We refer to
these as diagonal outcomes. We then compare the percentage of diagonal outcomes to the
percentages of selfish and cooperative outcomes. We classify the outcome according to which
9
See the appendix for robustness checks on this and all other parameter settings
14
of these three categories has the largest percentage. If the diagonal category, has the largest
percentage and if neither off diagonal box occurs more than twice as often as the other, we
classify the outcome as alternating. If one diagonal outcome is more than twice as likely, we
classify, the outcome as asymmetric.
In figure 1, we plot those outcomes using barycentric coordinates. We classify (C, S) and
(S, C) as off diagonal outcomes which allows us to display the outcomes from each game
in a two dimensional simplex, where the three possible outcomes are cooperate (CC), selfish
(SS), and diagonal (CS) and (SC).
Diagonal
TR ,BL = (0,0,1)
ALT =(0,.86,.14)
KE =(.3,.67,.03)
PD =(1,0,0)
SH =(0.97,.01,.02)
SI= (0,1,0)
Cooperative
Selfish
Figure 1: Simplex Representation of the Outcome Distributions for the Six Games
In each game, a joint payoff maximizing outcome is achieved nearly every time. And,
only in the Knife Edge and Alternation games do we see variation in the outcomes. We
can further unpack the outcomes in these two games by computing how often the outcome
results in an alternating strategy between the off diagonals in which each player receives the
same average payoff and how often the players settle into an asymmetric equilibrium. Those
15
results are shown in figure 2.10 In each game, approximately, two thirds of the time, the
agents are able to learn to alternate.
0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Cooperative
Asymmetric
Alternating
Knife Edge
Alternation
Selfish
Figure 2: Strategies used in Knife Edge and Alternation Game
Set Dependence
Given these baseline results, we next explore the extent to which see set dependence. We
explore set dependence in both outcomes and behaviors. We focus here first on the effect
of various initial games on two games: Knife Edge and Stag Hunt. Doing so enables us
to demonstrate how and why set dependence of outcomes occurs as well as revealing how
behaviors drive that dependence.
We begin by showing the dramatic differences in outcomes that occur in Knife Edge
following different initial games in the sequence. Figure 3 shows the outcomes for the Knife
10
Strategies are classified by modal outcomes. A strategy was classified as asymmetric if one of the off
diagonal outcomes was more than twice as probable as the other.
16
Edge game given different initial games. When Knife Edge is the first game in the sequence,
agents playing Knife Edge produce approximately twice as much alternating outcomes as
cooperative outcomes, and about three times as many cooperative outcomes as asymmetric
outcomes. Thus, alternating outcomes are fifteen times as likely as asymmetric outcomes.
But, when the agents play Knife Edge after Bottom Left, asymmetric outcomes become
more likely. In fact, the agents arrive at asymmetric outcomes more than six times as
often as alternating outcomes. But then, when the agents play Knife Edge after Stag Hunt,
Prisoner’s Dilemma, or Self Interest, asymmetric outcomes almost never occur. And finally,
selfish outcomes prove to be rare occurrences in every setting except for when Knife Edge
follows Alternation.
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Knife Edge
ALT - KE
Cooperative
PD - KE
Asymmetric
BL - KE
SI - KE
Alternating
SH- KE
Selfish
Figure 3: Outcomes in Knife Edge Under Different Initial Institutions (100 trials)
Some of these results can be explained intuitively. In the Stag Hunt and Prisoners’
Dilemma games, the agents cooperate and that cooperation bleeds over into the Knife Edge
game. Similarly, in Bottom Left, the agents settle on an asymmetric outcome and that
17
outcome often is maintained in Knife Edge. But other results are less intuitive. Why, for
example, does playing the self interest game first make the agents more likely to alternate
than if they had not played any game at all. And why does playing Bottom Left first, make
the agents more likely to learn to cooperate.
To explain these less intuitive findings, we must look at the behaviors that produce them.
When Knife Edge is the initial game, the agents begin with arbitrary strategies and that
they then learn how to play each game. A natural way to represent those strategies relies on
how the agents’ behavior changes as a function of the agent’s own behavior and that of its
opponent. Recall that an agent can be thought of as having two mental states: one in which
it is being cooperative, and one in which it is being selfish. These mental states correspond to
the agents’ action. Given the agent’s action in the previous period, there exist four possible
transitions. First, the agent could remain fixed to the same action. An agent using Grim
Trigger would be fixed given the selfish action. Second, the agent could match the action
of its opponent. An agent using Grim Trigger matches if taking the cooperative action.
An agent playing Tit for Tat matches the action of its opponent when the agent defects as
well. Third, the agent could automatically switch to the other action. This transition rule
would be useful in the Alternation Game. Finally, the agent take the opposite action of its
opponent. This last transition rule will be useful in the Top Left and Bottom Right games
given that the agents would like to take opposing actions.
In figure 4, we plot a randomly drawn initial distribution of strategies using this classification of strategies. The size of the circles corresponds the propensity of the strategy.
Given that we generate these automata randomly, they’re evenly spread across the possible
classifications. As the agents evolve strategies, this distribution will change.
In figure 5, we plot the average automata after the agents have learned to play Knife Edge.
Three types of strategies tend to evolve: (match,fixed), (match, match), and (switch,match).
The first of these pairs encodes grim trigger (assuming the agents cooperate in the first period,
which they do). The second pair can encode either Tit for Tat or Alternating depending on
whether the two agents begin taking the same action or different actions. The third encodes
18
Switch
i
i
g
a
Opposite
c
c
c
g
Match
g
g
i
c
Fixed
c
c
c
g
Fixed
Match
Selfish
Opp
Switch
Cooperative
Figure 4: A Randomly Drawn Initial Behavior:
Alternating.
In figure 6, on the left we plot the distribution over automata after the agents have
learned to play Bottom Left, a game that advantages the row player on the right we plot the
distribution for the agents after they have learned to play Knife Edge given that there initial
behaviors were those learned for Bottom Left. Notice that when playing Bottom Left, the
agents tend to learn a behavior classified as (opposite, fixed). This strategy will cooperate
when the other agent is being selfish and remain selfish when being selfish. When the Knife
Edge game is played first, this pair of strategies rarely occurs. However, when Knife Edge
follows Bottom Left, a substantial percentage of the time, that behavior remains in place
when Knife Edge is played. The fact that when playing Bottom Left first, the agents learn
to be fixed when in the selfish state also explains why so much cooperation occurs when
agents start playing Knife Edge. Grim Trigger (represented as (match, fixed)) can induce
cooperation by severely punishing those who don’t.
A similarly strong behavioral spillover can be seen by comparing what behaviors the
agents learn to play in the Prisoners’ Dilemma to what they learn to play in Knife Edge
after first playing the Prisoners’ Dilemma. As shown in figure 7, in the Prisoners’ Dilemma
19
Switch
`
b
`
d
Opposite
`
a
`
`
Match
`
k
`
Fixed
b
m
e
Match
Opp
Selfish
Fixed
`
Switch
Cooperative
Figure 5: Behavior: Knife Edge (100 Trials)
Switch
`
`
`
`
Switch
`
`
`
`
Opposite
b
`
i
`
Opposite
`
d
`
`
Match
`
`
`
Match
`
e
`
c
Fixed
k
`
Fixed
h
m
Selfish
`
#
`
"!
Fixed
Match
Opp
Switch
Fixed
Match
`
Opp
Switch
Cooperative
Figure 6: Behavior: Bottom Left and Knife Edge Following Bottom Left
20
Switch
a
Opposite
a
Match
a
Selfish
Fixed
b
Fixed
g
h
Match
`
`
Switch
`
b
`
b
`
`
Opposite
`
a
`
`
`
`
Match
`
`
`
Fixed
b
Opp
Switch
Fixed
Match
`
`
Opp
`
Switch
Cooperative
Figure 7: Behavior: Prisoners’ Dilemma and Knife Edge Following Prisoners’ Dilemma
the agents learn match in the cooperative state. In the selfish state, they may play fixed
(Grim Trigger), match (Tit for Tat), switch (Punish Once), or opposite (Win Stay, Lose
Shift). Each of these behaviors produces cooperation. When the agents learn to play Knife
Edge after having played the Prisoner’s Dilemma, many of these behaviors remain.
A close look at figure 7 also reveals why playing Knife Edge following the Prisoners’
Dilemma produces almost no asymmetric outcomes. Asymmetric outcomes require agents
to be fixed or play the opposite in each state. After playing the Prisoners’ Dilemma, almost
all of the agents learn to match in the cooperative state. Given that mutual cooperation
produces a good payoff, and that cooperating when the other is selfish does not, this behavior
will only be abandoned if the other player introduces an alternating strategy.
We know turn to set dependence for outcomes in Stag Hunt. Recall that when Stag Hunt
is the first game in the sequence that the agents always learned to cooperate. In figure ??,
we show the percentage of selfish outcomes for Stag Hunt following each of five games.
But when Stag Hunt follows Self Interest, approximately ten percent of the time, the
agents remain selfish. This is to be expected. In the Self Interest game the agents learn to
be selfish and this behavior is not always unlearned in Stag Hunt. But, quite surprisingly,
21
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
PD-SH
KE-SH
SI-SH
BL-SH
ALT-SH
Figure 8: Percentage of Selfish Outcomes in Stag Hunt (100 trials)
when Stag Hunt follows Bottom Left of Top Right, thirty percent of the time the agents
learn to be selfish in Stag Hunt, a nearly three fold increase over the level of selfish outcomes
following Self Interest. To see why, we need only look at the behaviors in the games.
Figure 9 shows behavior in Stag Hunt when it is the first game in the sequence. Agents
learn to play either be fixed or match in the cooperative state. It doesn’t really matter what
they do in the selfish state as that is not reached.
Figure 10 shows behavior following Bottom Left and behavior following Self Interest.playing
Bottom Left, the agents often learn opposite in the cooperative state. They, in effect, learn
to take turns - to do the opposite of what the other player does. So, if the other player
cooperates, the agent will then be selfish. This behavior produces selfish behavior in the
Stag Hunt game. In contrast, when agents learn the Self Interest game, they learned fixed
behavior in the selfish state but they’re no more likely to learn opposite behavior in the
cooperative state than any other behavior. This makes agents more likely to learn to be
cooperative following self interest rather than less likely.
A similar intuition explains why there exists more selfish play in Stag Hunt following
Alternation. Agents who first play alternation often learn either opposite or switch behavior
22
Switch
f
g
`
`
Opposite
d
l
`
`
Match
e
e
`
`
Fixed
c
m
`
`
Selfish
Fixed
Match
Opp
Switch
Cooperative
Figure 9: Behavior: Following Stag Hunt (100 Trials)
Switch
`
`
`
`
Switch
`
`
`
`
Opposite
b
`
i
`
Opposite
`
`
`
`
Match
`
`
`
Match
c
d
e
d
Fixed
k
`
`
Fixed
j
j
k
i
Selfish
`
#
"!
Fixed
Match
Opp
Switch
Fixed
Match
Cooperative
Figure 10: Behavior: Bottom Left and Self Interest
23
Opp
Switch
Switch
`
b
`
h
Opposite
`
`
`
`
Match
`
f
`
Fixed
b
`
Selfish
Fixed
Match
`
Opp
Switch
Cooperative
Figure 11: Behavior: Following Alternation Game (100 Trials)
in the cooperative state. (See figure ). Switching to selfish behavior immediately after
cooperating makes it more difficult for cooperation to emerge.
Path Dependence
The previous results demonstrated set dependence of outcomes and of behaviors. We now
explore the extent to which our model produces path dependence. Path dependence exists
if the same games played in a different order produced distinct outcomes and behaviors. We
begin our analysis by considering two pairs of games that include the Alternation game and
another game. We first analyze Knife Edge and Alternation. The second pair consists of
Stag Hunt and Alternation.
In figure 12, we show outcomes in Knife Edge and in Alternation when Knife Edge is
played first and when Alternation is played first. The graph on the top shows outcomes for
Knife Edge. When agents play Knife Edge second, they are far less likely to cooperate and
are more likely to alternate or to act selfishly. The graph on the bottom shows that when
Alternation is played second, individual are much more likely to alternate.
These may seem like minor differences, but notice that when Alternation is played first,
24
0.8
0.6
0.4
0.2
0
Cooperative
Asymmetric
Knife Edge (1)
Alternating
Selfish
Knife Edge (2)
1
0.8
0.6
0.4
0.2
0
Cooperative
Asymmetric
Alternation (1)
Alternating
Selfish
Alternation (2)
Figure 12: Path Dependent Outcomes in Knife Edge and Alternation (100 trials)
more selfish behavior occurs in both games, resulting in lower payoffs than if Alternation is
played second. Therefore, it is better to play Knife Edge first and then Alternation rather
than playing Alternation first and then Knife Edge. The reason for this is that Alternation
produces some selfish behavior which then gets learned in Knife Edge. When Knife Edge is
played first, the agents never learn to be selfish which reduces the amount of selfish behavior
in Alternation. This can be seen at an even deeper level by referring back to figure 5. Notice
that when Knife Edge is played first, the agents almost never learn the opposite behavior.
Next, we consider the pair of games Alternation and Stag Hunt. Figure 13 shows the
outcomes in Stag Hunt and Alternation game when Stag Hunt is placed first in the sequence
and when it is placed second.
When Stag Hunt is played first, the agent are much more likely to learn to be cooperative
than if it occurs after the Alternation game. The reason for this is that when Alternation is
played first, the agents sometimes learn to switch when in the cooperative state and this is
difficult to unlearn and results in selfish behavior in Stag Hunt.
This unfortunate spillover would seem to argue for playing Stag Hunt first. And in fact,
this is true. In fact, if Stag Hunt is played first, the agents are also more likely to alternate
25
0.8
0.6
0.4
0.2
0
Cooperative
Asymmetric
Knife Edge (1)
Alternating
Selfish
Knife Edge (2)
1
0.8
0.6
0.4
0.2
0
Cooperative
Asymmetric
Alternation (1)
Alternating
Selfish
Alternation (2)
Figure 13: Path Dependent Outcomes in Stag Hunt and Alternation (100 trials)
and less likely to be selfish in the Alternation Game. So, once again, we see path dependence
in the performance of institutions.
Institutional Path Dependence
Having demonstrated path dependence of both behaviors and outcomes, we now extend the
analysis and discuss how behavioral spillovers might produce institutional path dependence.
In the previous section, we have shown that the performance of an institution can depend
on the previous institutions because of behavioral spillovers. If a particular institution won’t
perform well following a prior institution or set of institutions, then we can assume that the
institution won’t be chosen. This could occur because the society has the foresight to know
it won’t function well or because the institution is tried, fails, and is replaced with one that
performs better.
The existence of two previous games implies that agents have a larger repertoire of
behaviors from which to choose an initial strategy. Here, we will assume that in the third
game, each agent randomly chooses either its strategy in the first game or its strategy in the
26
second game.11 . This construction assumes that the agents see all pairs of games as equally
similar, admittedly a strong assumption, but a reasonable starting point.
What explore the extent to which institutions are path limiting, i.e. the percentage of
paths of institutional choices that are inefficient. To make this assumption formal, we will
assume that if given an institutional context the efficient equilibrium is located five percent
less often than if the game were played alone, then the game will not be chosen. Formally,
we will say that a path is inefficient if efficiency falls by at least five percent. For example, in
the Knife Edge game, the efficient equilibrium is almost always learned. But, if Knife Edge
follows the Alternation game, then the selfish outcome is learned more than five percent of
the time. We therefore will assume that if the Alternation game is chosen first that Knife
Edge will not be chosen second.
With seven possible games and there exists three hundred and forty-three possible sequences of length three. Given an initial game, there exist forty-nine possible two game
continuation sequences. In figure 14, we show all possible sequences following the Prisoners’
Dilemma game.
Not all of these paths may be efficient. In figure ??, we erase the inefficient paths
following the Bottom Left Game.12 . What’s clear from the figure is that Bottom Left limits
the possible institutional sequences.
In figure 16, we show the efficient paths following the Prisoners’ Dilemma game. Notice
that many more paths are possible. The Bottom Left game is much more path limiting
than the Prisoners’ Dilemma. The reason for this is that the Prisoners’ Dillam produces
diverse behaviors in the selfish state. That diversity enables the agents to learn the efficient
equilibrium for other games. They’re less likely to be stuck in the basin of a bad equilibrium. In contrast, in Bottom Left, agents learn similar behaviors. This increased behavioral
coherence in each state hinders exploration. Thus, we find value in diverse behaviors within
a game because it aids learning.
11
An alternative assumption would be that the agents choose the behavior from the the game that’s most
similar to the new game. See Bednar and Page (2014)
12
This graph currently relies on a very small number of trials and inferences from two game sequences
27
SI
SH
TR
TR
ALT
PD
PD
ALT
PD
KE
ALT
SH
BL
SH
BL
SI
BL
SH
TR
KE
KE
ALT
TR
PD
SI
SH
BL
SI
BL
SI
TR
SI
SH
TR
BL
PD
PD
ALT
KE
SI
SI
SH
TR
BL
AL
ALT
PD
KE
SH
TR
PD
BL
KE
KE
ALT
PD
KE
Figure 14: The Forty-Nine Possible Paths Following PD as Initial Game
The assumption that agents initially choose the behavior of only the nearest game is
a strong assumption. People might well differ in which games they believe to be near to
one another leading them to choose different initial behaviors. This diversity of behaviors
from which to choose will also increase the likelihood of more efficient equilibria (at least in
the games that we consider here). Therefore, ideal sequences of institutions should produce
diverse behavior both within and across games. This second intuition echoes the Bednar and
Page (2014) results that early institutions should be diverse to build up diverse repertoires.
Discussion
Our results demonstrates an interplay between behavior, institutional outcomes, and institutional choice within a model. The results suggest that behavioral spillovers could lead to
institutional path dependence: behavioral repertoires. This explanation complements existing models of institutional path dependence that focus on increasing returns as well as
those that consider negative externalities (Pierson 2000, 2004, Page 2006). For example,
what Pierson describes as increasing returns will often mean institutions that leverage similar behavior. And, the negative externalities that Page describes exist in our framework as
28
SI
SH
TR
BL
SI
SH
TR
TR
BL
BL
SH
BL
ALT
SH
PD
SI
BL
PD
KE
KE
ALT
TR
SI
ALT
SI
SH
TR
BL
PD
PD
ALT
KE
AL
PD
KE
KE
Figure 15: The Efficient Paths Following BL as Initial Game (approx)
incongruent behaviors that limit the set of efficient future paths.
In showing how institutions reinforce one another by relying on similar behavioral repertoires our paper links institutional choices with some dimensions of culture. This linkage
makes intuitive sense given that institutions have considerable influence over behaviors,
norms, and culture. Focusing on the micro level features of a society such as explicit behavior as we do here offers a path between the long-standing uncomfortable methodological
choice of searching for culture-free regularities or treating each situation as unique. The
choice between universalistic rational choice and area studies need not result in a dividing
up of outcome dimensions. It is not that some outcomes – say, the number of political
parties – can only be explained by rational choice models and other outcomes – rates of
corruption – require an appeal to culture. Instead, within-country outcomes, whether regular or country-specific, can emerge as consistent with both purposive action and a cultural
context.
Thus, within our model, we see cultural behavior as emergent and not at all irrational.
Rather, it may be contextually rational, or as close to it as people might assume. The fact
that behavior may depend on context does not imply that we should abandon formal models
29
SI
SH
TR
TR
ALT
PD
PD
ALT
PD
KE
ALT
SH
BL
SH
BL
SI
BL
SH
TR
KE
KE
ALT
TR
PD
SI
SH
BL
SI
BL
SI
TR
SI
SH
TR
BL
PD
PD
ALT
KE
SI
SI
SH
TR
BL
AL
ALT
PD
KE
SH
TR
PD
BL
KE
KE
ALT
PD
KE
Figure 16: The Efficient Paths Following PD as Initial Game (approx)
or the search for regularities. To the contrary, our results suggest the value of building more
and better models and for doing even more experiments.
If we could understand what holds generally — free labor markets and central bank
independence leads to stable growth (Franzese 2002) — and what depends upon country
level factors — a tradition of cooperative behavior may be more conducive to democratic
institutions than a tradition of selfish behavior — then we can reach deeper understandings
and can design better institutions and policies. Ideally, social science will be able to explain regularities as well as country level differences in institutional evolution, selection, and
performance.
We see this framework as demonstrating proof of concept of a behavioral based approach
to understanding variation in institutional performance and institutional path dependence.
We do not see the results of this model or of related models such as Bednar and Page (2014)
a providing definitive explanations. Models based on beliefs or belief systems that drive
disparate institutional performances can produce related, but distinct insights13 Future work
will be necessary to unpack the differences between our behavior centric approach and belief
13
See Greif (1994, 2006), Grief and Laitin (2004), and Putnam 1993.
30
centric models. Moreover, our current model should be explored in more general contexts.
Extensions might include more realistic institutional structures and might also elaborate
how people are connected, how they categorize the world, what they believe, and how they
construct and interpret symbols.
In constructing richer models, we can guide case study research that may validate or
dispute the intuitions fleshed out in this model. Existing accounts support our core logic
even though they were not undertaken with that goal in mind. For example, the experiences
of Kazakhastan, Kyrgyzstan, and Uzbekistan reveal evidence of behavorial regularities on
institutional performance. (Jones Luong 2002). When freed of the shackles of the Soviet
system, these Central Asian countries did not revert to clan-based representational systems.
All chose regionally based electoral systems that mirrored the Soviet system that had been
in place. This implies that the culture, broadly speaking – here we include identity, connectedness, and belief systems, along with behavioral routines – were regionally-based not
clan-based. These regionally based behaviors and attitudes influenced the choice over informal electoral institutions. Electoral reforms put in place by Gorbachev as a result of his
policies of Glasnost and Perestroika which created regional power within the former states
had an impact on the culture, on what institutions would perform well, and, so it appears,
what institutions would be chosen when the opportunity arose.
Research on interethnic conflict and cooperation is also telling. Afri (2000) has demonstrated that interethnic cooperation emerges and persists even when agents care little about
the future and lack punishment mechanisms. These results fly in the face of isolated, single
game analysis but align with the sequential game model presented here. Our model suggests
that groups that are cooperative are more likely to select institutions that reward cooperation, which in turn further encourages future cooperation. Relatedly, Fearon and Laitin
(1996) show that interethnic cooperation, once established, is likely to persist even after
institutional mechanisms for cooperation are removed.
Relatedly, Karl (1997) has suggested that oil-rich states have trouble developing diverse
markets because the benefits that accrue from oil hinder the efficacy of markets to create
31
incentives to innovate. Grzymala-Busse (forthcoming) has found significant variation in the
performance of stock markets in Eastern Europe based upon the timing of the introduction
of regulatory institutions relative to stock markets. When market behavior was allowed
to develop in the absence of regulation, regulation was much less effective once introduced
than if behavior had developed with regulatory oversight from the start. Greif (1994, 2006)
shows that institutional performance depends on the characteristics of societies – the trustbased, segregated economic relations of the 11th century Maghribi worked well as long as the
trading circle was small, but the individualistic 12th century Genovese had institutions in
place to enforce contracts, giving them the advantage in long-distance trading. All of these
explanations for divergent development trajectories share an emphasis on diverse behavioral
responses to institutions. The framework we’ve presented here can explain the emergence of
behavioral consistencies that drive these diverse histories.
Finally, though our analysis and discussion have focused on societal level institutional
effects, we can observe our logic at work in organizational contexts as well. The corporate
culture literature provides many examples of path dependent choices (Cohen and Sastry
2000). Organizational theorists refer to the importance of early stages in corporate culture
formation as imprinting. Empirical evidence of imprinting has been found in craft unions,
department stores, banks, newspapers, and high-tech firms (Stinchcombe 1965, Swaminathan
1996, and Boeker, 1989). Imprinting applies to routines and learning rules (Cohen and
Bacdayan 1994). Ebay’s method of auctioning off goods has become prevalent because so
many people have evolved strategies for playing in that game. Holbrook et al. (2000)
similarly notes that visions for the future can be very much limited by past experiences.
As Clark (1997) reminds us, “nature is heavily bound by achieved solutions to previously
encountered problems” (p. 81). Thus, when choosing or designing an institution, we should
not limit attention to the equilibria it implements, we should also consider existing individual
and collective behavioral repertoires, and we should consider the effect of the institution on
those repertoires.
32
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