The Customary International Law Supergame February 23, 200 sufficient provocation to cause others to deviate forever in response: to kill the rule multilaterally The theoretical problem with grim trigger is that because it is collectively irrational it is not"renegotiation-proof. *4 That is, after a defection, a coalition of states will have incentives to come together and cooperate with the defector, depriving the grim trigger of credibility and therefore effectiveness. The reasoning is that equilibrium strategies that enforce cooperative outcomes by the use of this type of punishment can be undermined by the deviator offering to renegotiate, proposing that the punishment phase be abandoned in favor of a return to cooperation: a"let bygones be bygones"argument. 46 An obvious counterargument to this, of course, is that renegotiation unravels by"forward induction. " That is, once the players understand that defection and promises of future compliance will go on indefinitely, would they not decline to renegotiate the first time? Also, in the CIL context, we are operating on the assumption that states do not have the ossibility of forming binding agreements through renegotiation, preventing thi indefinite defection nevertheless, there may be circumstances in which such renegotiation is possible, and the offer to renegotiate and abide by the results is credible. If so, an alternative renegotiation-proof equilibrium is needed. We offer the penance strategy described below as a"weakly renegotiation proof alternative enance treat while a precise definition of renegotiation-proofness has not yet been agreed,the treatment by Farrell and Maskin is worth considering. They define a"weak perfect strategy profile. Using this definition, the grim trigger strategy profile is no o renegotiation proof"(WRP)equilibrium for an infinitely repeated game to be a subgan perfect equilibrium strategy profile that is not Pareto-dominated by any other subgan WRP, since after defection the payoffs to cooperation Pareto-dominate those of punishment. If renegotiation is possible and credible, the states will prefer to renegotiate after a defection 45 See, e.g., Joseph Farrell Eric Maskin, Renegotiation in Repeated Games, 1 GAMES econ BEHavior (1989); Fudenberg Tirole, supra note 36, at 174 Indeed, this is not uncommon in international law discourse. See, e. g, Scott M Sullivan, Changing The Premise of International Legal Remedies: The Unfounded Adoption Of Assurances And Guarantees Of Non-Repetition, 7U.C. L.A. J INT'L L. FOR AFF.265(2002-2003 Barrett notes that collective rationality is less of an issue in the field of domestic antitrust law, because renegotiation of an agreement in restraint of trade is illegal Barrett, supra note 44, at 11 48 Farrell Maskin, supra note 45The Customary International Law Supergame February 23, 2004 16 sufficient provocation to cause others to deviate forever in response: to kill the rule multilaterally. The theoretical problem with grim trigger is that because it is collectively irrational it is not “renegotiation-proof.” 45 That is, after a defection, a coalition of states will have incentives to come together and cooperate with the defector, depriving the grim trigger of credibility and therefore effectiveness. The reasoning is that equilibrium strategies that enforce cooperative outcomes by the use of this type of punishment can be undermined by the deviator offering to renegotiate, proposing that the punishment phase be abandoned in favor of a return to cooperation: a “let bygones be bygones” argument. 46 An obvious counterargument to this, of course, is that renegotiation unravels by “forward induction.” That is, once the players understand that defection and promises of future compliance will go on indefinitely, would they not decline to renegotiate the first time? Also, in the CIL context, we are operating on the assumption that states do not have the possibility of forming binding agreements through renegotiation, preventing this indefinite defection. 47 Nevertheless, there may be circumstances in which such renegotiation is possible, and the offer to renegotiate and abide by the results is credible. If so, an alternative “renegotiation-proof” equilibrium is needed. We offer the penance strategy described below as a “weakly renegotiation proof” alternative. iv. Penance While a precise definition of renegotiation-proofness has not yet been agreed, the treatment by Farrell and Maskin is worth considering. 48 They define a “weak renegotiation proof” (WRP) equilibrium for an infinitely repeated game to be a subgame perfect equilibrium strategy profile that is not Pareto-dominated by any other subgame perfect strategy profile. Using this definition, the grim trigger strategy profile is not WRP, since after defection the payoffs to cooperation Pareto-dominate those of punishment. If renegotiation is possible and credible, the states will prefer to renegotiate after a defection. 45 See, e.g., Joseph Farrell & Eric Maskin, Renegotiation in Repeated Games, 1 GAMES & ECON. BEHAVIOR (1989); Fudenberg & Tirole, supra note 36, at 174. 46 Indeed, this is not uncommon in international law discourse. See, e.g., Scott M. Sullivan, Changing The Premise Of International Legal Remedies: The Unfounded Adoption Of Assurances And Guarantees Of Non-Repetition, 7 U.C.L.A. J. INT’L L. & FOR. AFF. 265 (2002-2003). 47 Barrett notes that collective rationality is less of an issue in the field of domestic antitrust law, because renegotiation of an agreement in restraint of trade is illegal. Barrett, supra note 44, at 11. 48 Farrell & Maskin, supra note 45