Nash Equilibrium and International Law

Jens David Ohlin - Cornell University

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Game theory has transformed international law scholarship.  Recent accounts have harnessed alleged lessons learned from game theory in service of a new brand of realism about the field.  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.  These arguments can be distilled to the following elements: effective multilateral agreements are rarely achieved, either in treaty or customary form; most states consent to international legal norms through a process of bilateral agreements with specific partners who, in turn, have their own set of overlapping bilateral agreements; and compliance with these agreements, whether via treaty or customary law, is usually based on considerations specific to a particular partner rather than general considerations regarding the content of the legal norm.  In other words, states comply with international norms in specific interactions with a particular state if good reasons exist to believe that the other state will reciprocate such compliance.  This explains why a state might adhere to a particular legal norm with one partner but not with another.  According to this school of thought, the vast majority of the content of international law fits this paradigm as opposed to one that posits general legal obligations to the entire world community.  International legal relations are built around the self-interested behavior implicit in the Prisoner’s Dilemma, not the opinio juris—a sense of legal obligation—that public international lawyers take to be an essential ingredient in the formation of customary international law.

I argue that the new realism about international law suffers from a profound misunderstanding about the significance of game theory.  In short, the new realism misuses the methodology by concluding falsely that self-interested behavior and normativity are mutually exclusive.1  Indeed, that is the conclusion that the new realists draw from the Prisoner’s Dilemma.  This conclusion is false.

Goldsmith and Posner view international cooperation as a bilateral repeated Prisoner’s Dilemma, but international law is best understood as a Nash Equilibrium—a focal point that states gravitate toward as they make rational decisions regarding their strategy in light of strategies selected by other states.  Game theory defines a Nash Equilibrium as a solution in which each player evaluates the strategies of their competitors and decides that they gain no advantage by unilaterally changing strategy when all other players keep their own strategies unchanged.  A Nash Equilibrium functions as a kind of focal point, where participants in the game gravitate toward a particular legal norm and choose “compliance” as their strategy if and only if the other players in the game are also choosing compliance as their strategy.  When a bilateral international agreement works, one state realizes that unilaterally choosing “breach” as its strategy would confer no benefit because the costs associated with that shift in strategy are too costly.  So, the player sticks with compliance.  If one player decides that a shift in strategy (i.e., breach) is indeed in his or her best interest, then the players fall out of Nash Equilibrium.

When rational actors form international law by moving towards Nash Equilibria, does that indicate that they are acting out of self-interest and not out of the legal obligation implicit in the notion of opinio juris?  The conclusion follows from the premise only if self-interest and obligation are mutually exclusive categories, which they are not.

The best way to understand this point is to consider rational contractarianism, the theory developed by the philosopher David Gauthier to explain the formation of moral systems among rational actors.2  According to Gauthier, rational agents must make decisions based on the expected moves of their competitors.  Although the best possible outcome for a given player is defection in the face of compliance by all other competitors in the game, this outcome is also the outcome preferred by one’s competitors.  If all competitors defect, the resulting payoff is extremely low, effectively throwing the game back into a state of nature where no one complies with any moral constraints, thus producing the worst possible outcome.  The rational solution to the game, therefore, requires acceptance of the objectively second-best (but, rationally, only possible) outcome: acceptance of reciprocal moral constraints on behavior.  The purchase one gets from game theory is that self-interested behavior demands this acceptance.  Rational agents seeking to maximize their own outcomes will choose moral outcomes as long as morality is a group endeavor.

Of course, this still leaves unresolved the cleavage between the rational agent at the social bargaining table—who is rationally compelled to accept reciprocal moral constraints—and the rational agent who must decide whether or not to comply with the social contract.  It is one thing to demonstrate the rationality of bargaining for moral constraints, and quite another to demonstrate the rationality of ex post compliance with the results of the social contract.  For Gauthier, such a rational agent must be considered a constrained maximizer, or an agent who “enjoy[s] opportunities for co-operation which others lack,” as Gauthier puts it, as opposed to a straightforward maximizer.  The question is whether the constrained maximizer receives cooperative benefits that outweigh the risks associated with the strategy of constrained maximization—i.e., the risk that competitors in the game will defect and reject compliance as their strategy.

One can see how the strategy of constrained maximization is directly applicable to international legal relations.  When one state decides on a strategy for diplomatic relations, it can choose to be a straightforward maximizer or a constrained maximizer.  However, deciding to be a straightforward maximizer—although initially an attractive option—carries severe costs.  A state that pursues this strategy will be branded a rogue nation and deprive itself of the benefits associated with cooperative constraints.  Operating outside of the community of nations carries enormous costs, as North Korea, Iran, and other isolationist states can no doubt confirm.  Those who adopt a strategy of reciprocal commitments to international law not only live in a world of relative security—fewer military interventions and aggressive acts—but also a world of bilateral treaty arrangements that would otherwise be unavailable to them.  The rub of the argument is that the alleged dichotomy between fidelity to international law and self-interested behavior turns out to be illusory.  The fact that states are self-interested in no way undermines the normativity of international law.

However, this still leaves a theoretical tension between the demands of rationality (occasional defection) and the demands of law or morality that counsel adherence to principle even in the face of rational opportunism.  For Goldsmith and Posner, there is no moral basis to tell a state to follow international law when rational self-interest counsels in favor of defection.  And if indeed there arises a situation where the gains of defection outweigh the loss of cooperative opportunities at any given moment, rational choice would appear to demand defection.  And since our account of morality is closely linked with rational choice, there would appear to be no basis to tell a nation to forego self-interest in favor of principle.

Gauthier’s initial answer to this conundrum was to frame his account in terms of dispositions to cooperate—dispositions that were themselves rational (and moral) insofar as one found oneself in a community with a sufficient number of agents who were similarly disposed.  In later works, Gauthier pushed beyond the concept of dispositions to cooperate in favor of an account of agency that linked intentions with plans and strategies that operate over time.  In other words, although a naïve version of rational choice theory considers an agent’s all-things-considered judgment at each cardinal point in time, rational human agency operates in a far more subtle way.  Were rational agents to recalculate rational choice at every cardinal time point, the process of deliberation would exhaust and weigh them down to the point of total collapse—literally, paralysis by analysis.

Instead, rational agency should be understood in terms of strategies selected after moments of deliberation, after which the chosen strategies only come up for reevaluation at certain moments in time.  What is missing from the work of the new realists, in other words, is the concept of plans.  And, plans are sticky in the sense that rational agents form an intention to follow a plan and do not give up the plan at the drop of a hat.  Living life as a rational agent requires the use of plans; rational agency would be unimaginable without them.  Pursuing the strategy of rational choice at each cardinal time point may turn out to be less effective than choosing an overall strategy or plan that is rationally justified and then sticking to it.  Indeed, consistently pursuing rational choice at each time point may end up being self-defeating in the long-run.  Plans provide stability for agents to pursue long-term interests and should only be abandoned in favor of new plans, not in favor of momentary and isolated desires.  An agent that is too easily lured from a stable plan by opportunistic defection is a myopic chooser.  Another way of stating the point is that the rationality of compliance with the reciprocal constraint—following the rules and resisting the temptation to defect—is conditional on the constraint’s place within the larger, rationally justified plan.  [3.  See, e.g., Claire Finkelstein, Acting on an Intention, in Bruno Verbeek, ed., REASONS AND INTENTIONS 67, 83 (2008).]

There is strong reason to believe that states are rationally justified in pursuing a strategy of constrained maximization and sticking to it even when faced with the temptation of opportunistic defection.  Even if states could masquerade as principled—a doubtful proposition—constant defection from international legal norms may produce negative outcomes over time.  It might be more rational for states to pick the strategy that is rationally justified and stick to it: either try one’s best to engage with international institutions or ignore them.  Although it is unclear if this thesis could be empirically tested, it is very suggestive that the most successful nations in the world participate in international legal institutions, whereas rogue nations on the periphery often are beset with hunger, famine, and war.


Copyright © 2011 Cornell Law Review.

This editorial is based on Jens David Ohlin’s Article: Jens David Ohlin, Nash Equilibrium and International Law, 96 CORNELL L. REV. __ (forthcoming 2011).

Jens David Ohlin is a Professor of Law at Cornell Law School.

  1. Other commentators have noted the lack of support for this assumption.  The argument presented by Goldsmith and Posner relies on the proposition that customary international law is based on opinio juris and that acting in self-interest precludes acting out of a sense of legal obligation.  The answer to this skeptical challenge lies in properly understanding opinio juris as “the intent of states to propose or accept a rule of law that will serve as the focal point of behavior, implicate an important set of default rules applicable to law but not to other types of social order, and bring into play an important set of linkages among legal rules.”
  2. David Gauthier, Morals By Agreement (1986).

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