The Customary International Law Supergame February 23, 2004 methods, but by using the prisoners dilemma we hope to capture the essence of informal contracting under opposed interests. 32 One of the reasons that we choose this game is because it allows us to contextualize a number of insights and concerns that cannot easily be included in other analytical models. For example, we believe that the n-person prisoner's dilemma can take account of a number of the diverse considerations often referred to together as reputation"or "reputational sanctions. We also believe that the n-person prisoners dilemma must be at the core of a rationalist explanation of the effectiveness of social norms. Finally, we believe that the n-person prisoners dilemma offers parsimony: the factors that it takes into account seem necessary, and there are no factors that seem superflow In a non-cooperative, single-play circumstance, with a standard prisoners dilemma payoff structure, we would expect non-compliance. This is each player's dominant strategy, and a Nash equilibrium. This is because under the payoffs assumed in the prisoners dilemma, each party is better off defecting, no matter what the other party does. Therefore, under the rather restrictive assumptions of the true prisoner's dilemma, the parties each invariably choose the strategy that results in reduced individual welfare, and reduced aggregate welfare, compared to the non-defecting strategy. This is n inefficient outcome. By analogy, states playing the CIl game(assuming prisoner dilemma-type payoffs)in a bilateral single-play setting would fail to form or comply with a Cil rule that increased individual and aggregate welfare. Cooperation is strongly dominated, and the unique Nash equilibrium is for both states to defect. The same is true of a prisoner's dilemma game repeated a finite number of times known in advance to each period. "A subgame perfect equilibrium is a strategy profile that induces a Nash o the players. Now the unique sub-game perfect equilibrium is for each player to defect equilibrium in every subgame interest in this article is not so much in establishing CIL rules, as in enforcing then first mover advantages that would counteract the effect Fearon suggests. Finally, or For a discussion of the use of coordination games to model certain types of nternational contexts, see Barbara Koremenos, Charles Lipson, duncan Nidal Rational Design of International InstitutionS, 55: 4 INT'L ORG. 761, 774(2001); Dur Snidal, Coordination versus Prisoner's Dilemma: Implications for international Cooperation and Regimes, 79: 4 AM. POL. SCL. REV. 923(1985) See Guzman, supra note 2 STEPHEN MARTIN, ADVANCED INDUSTRIAL ECONOMICS 98(1993) a"dominant strategy"is one which, no matter what the other player does, will provide a higher payoff to the acting player. A" Nash equilibrium"is a set of"strategies h that each players strategy is an optimal response to the other players' strategies DREW FUDENBERG JEAN TIROLE, GAME THEORY 11(1991) ld. at 111 37 M.J. OSBORNE, AN INTRODUCTION TO GAME THEORY(Oxford University Press, 2004)The Customary International Law Supergame February 23, 2004 11 methods, but by using the prisoner’s dilemma we hope to capture the essence of informal contracting under opposed interests. 32 One of the reasons that we choose this game is because it allows us to contextualize a number of insights and concerns that cannot easily be included in other analytical models. For example, we believe that the n-person prisoner’s dilemma can take account of a number of the diverse considerations often referred to together as “reputation” or “reputational sanctions.” 33 We also believe that the n-person prisoner’s dilemma must be at the core of a rationalist explanation of the effectiveness of social norms. Finally, we believe that the n-person prisoner’s dilemma offers parsimony: the factors that it takes into account seem necessary, and there are no factors that seem superfluous. In a non-cooperative, single-play circumstance, with a standard prisoner’s dilemma payoff structure, we would expect non-compliance. 34 This is each player’s dominant strategy, and a Nash equilibrium. 35 This is because under the payoffs assumed in the prisoner’s dilemma, each party is better off defecting, no matter what the other party does. Therefore, under the rather restrictive assumptions of the true prisoner’s dilemma, the parties each invariably choose the strategy that results in reduced individual welfare, and reduced aggregate welfare, compared to the non-defecting strategy. This is an inefficient outcome. By analogy, states playing the CIL game (assuming prisoner’s dilemma-type payoffs) in a bilateral single-play setting would fail to form or comply with a CIL rule that increased individual and aggregate welfare. Cooperation is strongly dominated, and the unique Nash equilibrium is for both states to defect. 36 The same is true of a prisoner’s dilemma game repeated a finite number of times known in advance to the players. Now the unique sub-game perfect equilibrium is for each player to defect in each period. “A subgame perfect equilibrium is a strategy profile that induces a Nash equilibrium in every subgame.” 37 first mover advantages that would counteract the effect Fearon suggests. Finally, our interest in this article is not so much in establishing CIL rules, as in enforcing them. 32 For a discussion of the use of coordination games to model certain types of international contexts, see Barbara Koremenos, Charles Lipson, & Duncan Snidal, The Rational Design of International Institutions, 55:4 INT’L ORG. 761, 774 (2001); Duncan Snidal, Coordination versus Prisoner’s Dilemma: Implications for International Cooperation and Regimes, 79:4 AM. POL. SCI. REV. 923 (1985). 33 See Guzman, supra note 2. 34 STEPHEN MARTIN, ADVANCED INDUSTRIAL ECONOMICS 98 (1993). 35 A “dominant strategy” is one which, no matter what the other player does, will provide a higher payoff to the acting player. A “Nash equilibrium” is a set of “strategies such that each player’s strategy is an optimal response to the other players’ strategies.” DREW FUDENBERG & JEAN TIROLE, GAME THEORY 11 (1991). 36 Id. at 111. 37 M.J. OSBORNE, AN INTRODUCTION TO GAME THEORY (Oxford University Press, 2004)