Nash Equilibrium and International Law

Game theory has been a mainstay in the international relations literature for several decades, but its appearance in the international law literature is of a far more recent vintage. Recent accounts have harnessed alleged lessons learned from game theory in service of a new brand of “realism” about international law. 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. Such claims are not just vastly exaggerated; they represent a profound misunderstanding about the significance of game theory. Properly conceived, 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. In domains where international law has the greatest purchase, the preferred strategy is reciprocal compliance with international norms. This strategy is consistent with the normativity of both law and morality, both of which are characterized by self-interested actors who accept reciprocal constraints on action to generate Nash Equilibria and, ultimately, a stable social contract. These agents - “constrained maximizers” as the philosopher David Gauthier calls them - accept the constraints of a normative system in order to achieve cooperative benefits. This Article concludes by explaining that it is also rational for states to comply with these constraints: agents evaluate competing plans and strategies, select the best course of action, and then stick to their decision, rather than obsessively reevaluating their chosen strategy at each moment in time. A state that defects from international law when the opportunity arises may, in the long run, reduce its overall payoff, as compared to a state that selects and adheres to a strategy of con-strained maximization.