NASH EQUILIBRIUM AS A MEAN FOR
DETERMINATION OF RULES OF LAW
(FOR SOVEREIGN ACTORS)
Taron Simonyan1
Social behavior and relations, as well as relations of states in
international area, are regulated by rules most of which have
normative character. The 20th and 21st centuries can be
characterized also by the fact that the quantity of legal rules and
norms – trying to regulate all the above-mentioned relations and
behavior – have increased, sometimes in geometric progression. But
there are still some relations that are not regulated by written law or
clear customary norms, and in order to regulate those relations one
needs to determine rules of law in order to have a particular relation
regulated in a due manner. And some questions may arise here:
where have those rules and norms come from; what are the sources
of such rules; have those rules and norms come from other social
norms; are they transformed types of other social norms; how can
those rules be determined; what methodology can be used for that
determination, etc.?
If it is mostly clear that in the case of domestic affairs and
relations a sovereign state provides the norm of law either by the
parliament, by the executive power (in Civil Law countries), or by
the court (in Common Law countries), the situation is different with
respect to international relations, where the main source of
international law is the will of states, and the main means, stipulated
by the Statute of ICJ, are the forms reflecting that will of states:
a. international conventions, whether general or particular,
establishing rules expressly recognized by the contesting states;
b. international custom, as evidence of a general practice
1
Candidate of Legal Sciences, Assisting professor of the Chair of Theory and
History of State and Law of the Yerevan State University. E-mail:
[email protected]. 17
accepted as law;
c. general principles of law recognized by civilized nations.
The same article provides also the secondary means for the
cases when it is unclear where to find the crystallized will of states:
“judicial decisions and the teachings of the most highly qualified
publicists of the various nations, as subsidiary means for the
determination of rules of law”2.
In the present research I will concentrate on the issues of
determination of rules of international law and a small part of
domestic law (mainly in civil law, where the actors are relatively
sovereign); both of them will appear in the present research as “law”.
I will try to show that a very interesting foundation of the Game
theory, the principle or concept of Nash equilibrium, can have a very
useful and productive role for the due determination of rules of law,
which are difficult to find and apply, and try to make some
inferences on the paths of determination of rules of law.
The practice of the past fifty years shows that it is very hard to
determine rules of law by only the existing means. We need
something more, the missing elements or element, which can provide
more opportunities for researchers and practitioners to find and apply
the right norm. In this regard Dr. Eyal Benvenisti shows that the
existing means for the determination of rules of international law are
not enough and offers another vision: the vision on law from the
point of the efficiency: “the doctrine on customary international law
is inherently linked to the principle of efficiency. Efficiency justifies
the doctrine. Put differently, efficiency is the underlying principle –
the grundnorm – of customary international law.”3
This is a very innovative approach in theory of law and
especially in international legal studies, and it shows the necessity of
changing the paradigms on legal research and legal practice. One can
argue that by changing the paradigms we shift our point of view from
2
Article 38, 1, Statute of International Court of Justice. Eyal Benvenisti, Customary International Law as a Judicial Tool for Promoting
Efficiency; The Impact of International Law on International Cooperation,
Theoretical Perspectives, Cambridge University Press, 2004, pages 85-116. 3
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legal studies to philosophical studies, but it has already been
stipulated by several researchers and scientists that law, as such, is a
complex system and cannot be researched otherwise than through its
very complex, interconnected essence, using interdisciplinary vision,
if one needs to analyze its real role and features in social behavior.
And for deep, comprehensive research and analysis in the 21st
century, one needs new approach, new paradigm meeting the
requirements of the interconnected world where all elements are in a
process of synergy, and the whole is much more than just the amount
of its elements. This complex and interconnected reality in law can
be studied by new methodology, new theory that is the complexity
theory, as “[c]omplexity theory provides an analogical foundation
for that new paradigm of legal theory.”4
By using this vision “[o]ne might accept the presence of
invisible hands throughout social life and the value of using complex
adaptive systems theory to understand them better, but nonetheless
resist applying complex adaptive systems theory to legal systems on
the ground that the law is where humans write the rules for other
social systems. But this misses two fundamentals. First, the legal
system, as a source of rules for regulating other social systems,
should take into account how those systems operate. If one wishes to
regulate a complex adaptive social system, one ought to think like a
complex adaptive social system. Second, law, as in the collection of
rules and regulations, is the product of the legal system, a collection
of people and institutions. Law, in this sense, is simply an emergent
property of the legal system the same way prices are an emergent
property of markets.”5
When trying to understand new ways of determination rules of
law, which can show a broader vision to legal reality, I try to use the
benefits of the Game theory (Nash equilibrium) along with the
4
Ruhl. J. B., Complexity theory as a paradigm for the dynamical law-and-society
system: A wake-up call for legal reductionism and the modern administrative state,
Duke Law Journal, volume 45, 1996a, 849-928, page 906. 5
Ruhl. J. B., Law's Complexity, Georgia State University Law Review Symposium
Issue, Forthcoming, FSU College of Law, Public Law Research paper No. 313, 885911, page 897. 19
Complexity theory.
First of all, one must say that the Game theory has been a focal
point in research and studies of international relations for several
decades, but its appearance generally in law and particularly in
international law is of a far more recent vintage. As Jens David Ohlin
says, “the best way to understand international law is as a Nash
Equilibrium – a focal point that states gravitate toward as they make
rational decisions regarding strategy in light of strategies selected
by other states.”6
Nash equilibrium is a fundamental concept in the theory of
games and the most widely used method of predicting the outcome
of a strategic interaction in the social sciences. It is defined as “a
steady state of the play of a strategic game in which each player
holds the correct expectation about the other players’ behavior and
acts rationally.”7
Mathematician John Forbes Nash in his 1951 article, “NonCooperative Games”, was to define a mixed strategy Nash
Equilibrium for any game with a finite set of actions and prove that
at least one (mixed strategy) Nash Equilibrium must exist in such a
game. This concept was created in contradiction of Adam Smith’s
concept, according to which “in competition, individual ambition
serves the common good”, and that “the best result will come from
everybody in the group doing what's best for himself, and the group”.
Whereas John Nash, considering Adam Smith’s concept as
incomplete, adds the cooperation as an important tool to get the best
outcomes for each participant of the game, creating an equilibrium in
social or other behavioral environment.
Since the 1960s social scientists and political leaders have been
using the inferences of the Game theory to have a sophisticated
matrix for modeling state relations. Thomas Schelling was one to
6
Jeans David Ohlin, Nash Equilibrium and International Law, Cornell Legal Studies
Research Paper No. 11-20, Cornell Law Review, Vol. 96, pages 869-900, 2011,
page 869. 7
Martin J. Osborne & Ariel Rubinstein, A Course in Game Theory 14 (1994). 20
write a comprehensive research on this issue8. The theory is widely
spread also in econometrics, political science other social sciences.
And by this tool social scientists could not only explain why some
states had acted the way they did, but might also predict future
behavior under certain conditions9.
While game theory offered theorists of international relations a
model for explaining state relations, the methodology has had a far
more explosive effect among international lawyers. Recent accounts
have harnessed alleged lessons learned from game theory in service
of a new brand of realism about international law.10 These skeptical
accounts conclude that international law loses its normative force
because states that “follow” international law are simply participants
in a Prisoner’s Dilemma seeking to achieve self-interested
outcomes.11 States comply with international norms in specific
interactions with a particular state when there are good reasons to
believe that the other state will reciprocate such compliance.12
The new realists proceed to argue that compliance in a
Prisoner’s Dilemma is based on reciprocity that is hard to come by.
A state will prefer to violate the treaty or customary rule while their
competitor adheres to it, though this state of affairs is hard to achieve
as all competitors share the exact same preference.13
But in any case, most of the researches insist: “[t]he fact that
states are self-interested is no way undermines the normativity of
international law. In the end, states cooperate by complying with
international legal norms and this commitment is necessarily
grounded by their self-interest.”14
8
Thomas C. Shelling, The Strategy of Conflict, 3-20 (2nd ed. 1980). Joel. P. Trachtman, The Economic Structure of International Law, 4-5, (2008). 10
Jack L. Goldsmith & Eric A. Posner, The Limits of International Law (2005); Eric
A. Posner, Do States Have a Moral Obligation to Obey International Law?, 55 Stan.
L. Rev. 1901 (2003). 11
Jack L. Goldsmith & Eric A. Posner, ibid., page 184. 12
Jack L. Goldsmith & Eric A. Posner, ibid., pages 87-88. 13
Jack L. Goldsmith & Eric A. Posner, ibid., pages 32-35. 14
Jeans David Ohlin, Nash Equilibrium and International Law, Cornell Legal
Studies Research Paper No. 11-20, Cornell Law Review, Vol. 96, pages 869-900,
2011, pages 885. 9
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All this mean that if a sovereign actor, a subject of law, is
rational and holds the correct expectation about the other actors’
behavior, acts rationally, a new equilibrium will come to life, which
will have reciprocal agreement of all actors in its essence in a written
or non-written form. In this equilibrium all actors will benefit from
each other, no one will be defeated in the relation, no one will lose
from the “game”, and the system of social relations and behavior will
get some kind of its state of “pareto optima”, which can give rise the
efficiency of the whole system in itself and for all actors within,
increasing the system’s productivity.
Eyal Benvenisti in his essay on “Customary International Law
as a Judicial Tool for Promoting Efficiency” describes his view on
customary international law as a tool for international courts, mainly
International Court of Justice, to develop international law and
promote efficiency.
He stipulates: “when states or any other players interact, they
rationally find themselves in Nash equilibria that may be inefficient.
A judicial declaration of one equilibrium as the one that is binding
as custom is likely to lead all players to modify their activities to
conform to the judicially sanctioned equilibrium. This equilibrium
will thus become the new practice, the new custom. This suggests
that one state’s deviation from prior practice in favor of a more
efficient one need not be regarded as a breach if the deviation
conforms to the underlying norm of efficiency. Rather, such a
deviation has a very good chance of becoming, sooner rather than
later, and certainly with the help of an intervening court, the new
practice, the new norm.” And in the end he concludes: “[e]fficiency,
in the sense of efficient allocation of resources among states, has
been all along the driving force behind the development of
international law in general and customary international law in
particular. State practice has often proven a reliable proxy for
determining what constitutes efficient behavior for all states to
follow. This proxy enabled international tribunals and other actors
to impose sanctions on free riders or others seeking to deviate from
the efficient norm. But this proxy fails when global or regional
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conditions lead states to pursue inefficient behavior. In such
situations, tribunals and other third parties can make a difference by
pushing states towards new, more efficient Nash equilibria.” 15
The author takes the concept of “efficiency” as another mean for
determination of rules of law, especially customary law, and
describes Nash equilibrium as a set of relations that attracts state
practice and the “belief that this practice is rendered obligatory”16,
namely – “opinio juris”.
I offer to view to the reality of relations between the sovereign
actors (states or other actor, e.g. contracting parties in civil law
relations) from another point of view. When it is unclear where can
the rules of law be derived from, there is no apparent evidence of the
existence of customary international law, only the concept or
principle of efficiency cannot give the answer to risen questions. It is
the equilibrium of Dr. Nash that can contain in itself the path of lawcreation and law-development acceptable by all actors in a given
relationship, if these actors, of course, are rational and ready to act
rationally, which means that they want to earn the most benefits from
the system of relations and not just to do harm to other actors, even if
they get less from these relations. This means that Nash equilibrium
already contains in itself the most favorable efficiency for the actors
and the system as a whole. We should look at the set of social or
international relations from above, from the point of view of the most
favorable efficiency for that particular time, which in its case, can be
found only in Nash equilibrium.
Thus, Nash equilibrium is the driving force for the development
of international and social relations of rational actors, covering and
regulating system of law either international, or domestic. From this
vision one can make an inference that a subject of law, an actor,
15
Eyal Benvenisti, Customary International Law as a Judicial Tool for Promoting
Efficiency; The Impact of International Law on International Cooperation,
Theoretical Perspectives, Cambridge University Press, 2004, pages 85-116. 16
North Sea Continental Shelf (F.R.G. v. Den./Neth.), I.C.J. Reports 1969, page 3,
at para. 77. The Permanent Court of International Justice first enunciated the
doctrine of opinio juris in the Lotus Case (France v. Turkey), P.C.I.J. Reports, Series
A, No. 10 (1927) at 28. 23
while getting the highest level of satisfaction of his/her/its interests
and making the minimum inconvenience for other subjects/actors,
harmonizes his/her/its private interests with common interests and
makes a ground for relative equilibrium of the system, and the
center, foundation of that equilibrium becomes the focal point and
source of rules for common behavior, thus, rules of law of that
particular period of time.
This conclusion can be considered as a reflection of law’s
essence as the guarantee and expression of social equilibrium (as
well as equilibrium in supranational relationship) and sustainability.
The actors of a given relationship, if acting rational, will come to the
final conclusion of acting in cooperation regime, where synergy can
be reached and it can bring more satisfaction for the system as a
whole and for each participant in particular than if they act in pure
competition regime aspiring to get more at the expense of other
actors’ interests.
Therefore, bearing this position in mind, it is not hard to realize
the significant role of Nash equilibrium in the determination of rules
of law for relatively sovereign actors. And that role can be compared
with another concept of the theory of Complex Systems – the
concept of Attractor, which can be described as a set towards which
a variable, moving according to the dictates of a dynamical system,
evolves over time. And even if the social behavior or international
relations are slightly disturbed, while getting close enough to that
attractor, those relations and behavior will remain close to it. But this
can be a subject for another research.
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