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)