The Customary International Law Supergame February 23, 2004 perfect: after a defection, the wronged state will have incentives to accept an undertaking from the defecting state that it will cooperate in future. Subgame perfection means that at every stage of an iterated game, no player will have an incentive to deviate from the equilibrium strategy, even when others do. Even more devastating to tit-for-tat is the fact that once one state defects the game cycles endlessly between defection and compliance. li1. Grim Trigger Second, states may respond to defection with defection forever: a bilateral"grim trigger"strategy. There are two basic approaches that have been developed in the theory of repeated games. The first assumes that any deviation is met with a response that maximizes the loss that the deviator suffers-a" minmax" "strategy -even if this imposes costs on the punishers. The second approach assumes that deviation results in reversion to the one-shot Nash equilibrium of the prisoner's dilemma game. We adopt the latter approach since it appears to be more appealing to players. Essentially, we assume that in the event of deviation the states revert to the strategies that they would have adopted if no CiL rule had developed in the first place. The grim trigger strategy is subgame perfect, as it calls for a reversion to the dominant strategy of defection in response to an initial defection equilibria under certain circumstances where states play the grim trigger strategy i ent Goldsmith and posner appear to recognize the possibility for stable and effic However, using an overfishing of commons context as their example, they suggest that he grim trigger is not used and would be collectively irrational. In his interesting work on treaties relating to environmental commons problems, Barrett also rejects the grim trigger strategy because it fails to satisfy the criterion of collective rationality. The collective rationality consideration is a formal articulation of an intuitive concern that it would be extraordinarily wasteful to abandon an efficient multilateral agreement because of a single defection. While it would be individually rational to respond with defection forever--it is subgame perfect as the reversion to the Nash equilibrium--it is collectively irrational insofar as rational negotiators will have incentives to renegotiate a cooperative arrangement after defection With respect to the more empirical question of whether a grim trigger is used, if we think not about the cil that exists but about the cil that does not exist it is clear that states do play the grim trigger strategy at least in some contexts. In fact, one might argue that the multilateral grim trigger is the existing default strategy in CIL. That is where a Cil rule exists or is proposed for formation, and one state deviates, that may be 42l,at138 Goldsmith Posner 1999, supra note 2, at 1129-1130 Scott Barrett, A Theory of Full International Cooperation, ll J THEORETICAL POL 519(1999); SCOTT BARRETT, ENVIRONMENT AND STATECRAFT: STRATEGIES OF ENVIRONMENTAL TREATY-MAKING (2003)
The Customary International Law Supergame February 23, 2004 15 perfect: after a defection, the wronged state will have incentives to accept an undertaking from the defecting state that it will cooperate in future. Subgame perfection means that at every stage of an iterated game, no player will have an incentive to deviate from the equilibrium strategy, even when others do. Even more devastating to tit-for-tat is the fact that once one state defects the game cycles endlessly between defection and compliance. 42 iii. Grim Trigger Second, states may respond to defection with defection forever: a bilateral “grim trigger” strategy. There are two basic approaches that have been developed in the theory of repeated games. The first assumes that any deviation is met with a response that maximizes the loss that the deviator suffers – a “minmax” strategy – even if this imposes costs on the punishers. The second approach assumes that deviation results in reversion to the one-shot Nash equilibrium of the prisoner’s dilemma game. We adopt the latter approach since it appears to be more appealing to players. Essentially, we assume that in the event of deviation the states revert to the strategies that they would have adopted if no CIL rule had developed in the first place. The grim trigger strategy is subgame perfect, as it calls for a reversion to the dominant strategy of defection in response to an initial defection. Goldsmith and Posner appear to recognize the possibility for stable and efficient equilibria under certain circumstances where states play the grim trigger strategy. 43 However, using an overfishing of commons context as their example, they suggest that the grim trigger is not used and would be collectively irrational. In his interesting work on treaties relating to environmental commons problems, 44 Barrett also rejects the grim trigger strategy because it fails to satisfy the criterion of collective rationality. The collective rationality consideration is a formal articulation of an intuitive concern that it would be extraordinarily wasteful to abandon an efficient multilateral agreement because of a single defection. While it would be individually rational to respond with defection forever—it is subgame perfect as the reversion to the Nash equilibrium—it is collectively irrational insofar as rational negotiators will have incentives to renegotiate a cooperative arrangement after defection. With respect to the more empirical question of whether a grim trigger is used, if we think not about the CIL that exists, but about the CIL that does not exist, it is clear that states do play the grim trigger strategy at least in some contexts. In fact, one might argue that the multilateral grim trigger is the existing default strategy in CIL. That is, where a CIL rule exists or is proposed for formation, and one state deviates, that may be 42 Id., at 138. 43 Goldsmith & Posner 1999, supra note 2, at 1129-1130. 44 Scott Barrett, A Theory of Full International Cooperation, 11 J. THEORETICAL POL. 519 (1999); SCOTT BARRETT, ENVIRONMENT AND STATECRAFT: STRATEGIES OF ENVIRONMENTAL TREATY-MAKING (2003)
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 45
The 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