The Customary International Law Supergame February 23, 2004 The model we present here formalizes certain considerations that remain informal in much of the political science literature, and has other varying features that we describe 2. The N-Person prisoner's dilemma In this section we explain our choice of the n-person prisoner's dilemma as the basic model for the Cil problem, examine the potential strategies that might be played within this game, and explain some of our assumptions. The n-person iterated prisoner's dilemma is really a group of varying models, with a number of varying features including the number of players and their preferences a. Choice of game noted, As we consider the application of game theory to the Cil setting, it should be that there is a wide choice of potential game structures to apply. The basic payoff structure assumed in the prisoners dilemma game captures the essential problem of cooperation in a horizontal social setting with externalities, in which parties have a choice between compliance and defection under circumstances in which they can enrich themselves individually through defection while they could enrich society through compliance. Of course, some CIL contexts might be better modeled using other 577(1992); Joel P. Trachtman, The Domain of wTo Dispute Resolution, 40 HARV. INT'L LJ.333,346-47(1999) For a useful analysis of the "fit" of other games, including"battle of the sexes"and stag hunt, see Swaine, supra note 2. See also Fiona McGillivray Alastair Smith Trust and Cooperation Through Agent-Specific PunishmentS, 54 INT'L ORG. 809, 810 (2000)(noting that the prisoner's dilemma is often used to model international Coo peau y use of the term"externalities, "we mean to be quite inclusive, including both iniary and non-pecuniary externalities: any circumstance in which an action by one state has adverse or beneficial effects on another state At another level of complexity, it would be possible to model the game of formation of a Cil rule separately from enforcement. See James D. Fearon, Bargaining Enforcement, and International Cooperation, 52: 2 INT'L. ORG. 269(1998)(separating the bargaining problem, modeled as a coordination game, from the enforcement problem, modeled as a prisoners dilemma); Stephen D. Krasner, Global Communications and ational Power: Life on the Pareto Frontier, 43 WORLD POL. 336(1991)(arguing that many international issues are better modeled as coordination games). Fearon's two stage approach may be more appropriate to the treaty context than to the custom context Fearon points out that relatively large "shadows of the future "might inhibit bargaining to achieve an initial coordination game agreement, while making the enforcement game more tractable. In the CIl context, there is less natural separation, and there may even beThe Customary International Law Supergame February 23, 2004 10 The model we present here formalizes certain considerations that remain informal in much of the political science literature, and has other varying features that we describe below. 2. The N-Person Prisoner’s Dilemma In this section we explain our choice of the n-person prisoner’s dilemma as the basic model for the CIL problem, examine the potential strategies that might be played within this game, and explain some of our assumptions. The n-person iterated prisoner’s dilemma is really a group of varying models, with a number of varying features, including the number of players and their preferences. a. Choice of Game As we consider the application of game theory to the CIL setting, it should be noted that there is a wide choice of potential game structures to apply. 29 The basic payoff structure assumed in the prisoner’s dilemma game captures the essential problem of cooperation in a horizontal social setting with externalities, 30 in which parties have a choice between compliance and defection under circumstances in which they can enrich themselves individually through defection while they could enrich society through compliance. 31 Of course, some CIL contexts might be better modeled using other 577 (1992); Joel P. Trachtman, The Domain of WTO Dispute Resolution, 40 HARV. INT'L L.J. 333, 346-47 (1999). 29 For a useful analysis of the “fit” of other games, including “battle of the sexes” and “stag hunt,” see Swaine, supra note 2. See also Fiona McGillivray & Alastair Smith, Trust and Cooperation Through Agent-Specific Punishments, 54 INT'L ORG. 809, 810 (2000) (noting that the prisoner’s dilemma is often used to model international cooperation). 30 By use of the term “externalities,” we mean to be quite inclusive, including both pecuniary and non-pecuniary externalities: any circumstance in which an action by one state has adverse or beneficial effects on another state. 31 At another level of complexity, it would be possible to model the game of formation of a CIL rule separately from enforcement. See James D. Fearon, Bargaining, Enforcement, and International Cooperation, 52:2 INT’L. ORG. 269 (1998) (separating the bargaining problem, modeled as a coordination game, from the enforcement problem, modeled as a prisoner’s dilemma); Stephen D. Krasner, Global Communications and National Power: Life on the Pareto Frontier, 43 WORLD POL. 336 (1991) (arguing that many international issues are better modeled as coordination games). Fearon’s two stage approach may be more appropriate to the treaty context than to the custom context. Fearon points out that relatively large “shadows of the future” might inhibit bargaining to achieve an initial coordination game agreement, while making the enforcement game more tractable. In the CIL context, there is less natural separation, and there may even be