The Customary International Law Supergame February 23, 2004 This article refines and extends an emerging rationalist understanding of CIL Pioneering work in this field, notably that of Jack Goldsmith and Eric Posner, has begun to articulate a rationalist theory of CIL. Goldsmith and posner have argued that CIL(a) does not exogenously affect state behavior and (b) is internally incoherent, as states not motivated by opinio juris to comply with CiL.' We show why the first assertion is either tautological or incorrect as a matter of theory, and, to the extent that it purports to rely on factual observation, is not supported by the data presented. The tautology arises from a false dichotomy between motivation by self-interest and motivation by law. In a ationalist model, behavior is assumed to be motivated by self-interest. If law is artificially separated from self-interest, then of course a rationalist model would assume that law has no motivating force. Yet we show how CiL rules may modify the payoffs of behavior and therefore affect behavior through self-interest. While cil is endogenous to states as a group, it is an exogenous influence on the behavior of each individual state CIL may affect behavior even if it only does so at the margins. As to the second assertion, our analysis provides a plausible basis to assign a discriminating role to opinio juris, and therefore we find cil doctrine internally coherent in at least its core dimension This article develops an iterated multi-player prisoners dilemma model of CIL. Of course, game theory can only provide a crude representation of highly nuanced decision-making. Our analysis focuses on parameters of the multi-player prisoners dilemma in the CIL context: (i)the relative value of cooperation versus defection, (ii) the number of states effectively involved, (iii) the extent to which increasing the number of See, e.g., Mark A Chinen, Afterword, 23 MICH. J INT'L L 201(2001); Mark A Chinen, Game Theory and Customary International Law: A Response to Professors Goldsmith and Posner, 23 MICH. J INT'L L 143 (2001): Vincy Fon francesco Parisi, International Customary Law and Articulation Theories: An Economic Analysis, George Mason Law and Economics Research Paper No. 02-24, available at http:papersssrn.com/sol3/papers.cfm?abstractid=335220;JackL.Goldsmith&ericA Posner, Further Thoughts on Customary International Law, 23 MICH. J INTL L. 191 (2001); Jack L. Goldsmith& Eric A Posner, A Theory of Customary International Law, 66 U. CHI. L REv. 1113(1999) hereinafter Goldsmith Posner 1999]; Andrew T. Guzman, A Compliance-Based Theory of international Law, 90 CAL L REV. 1823 (2002); Francesco Parisi, The Formation of Customary Law, George Mason Law and Economics Research Paper No. O1-06, http:/papers.ssrn.com/sol3/papers.cfm?abstractid=262032;edWardt.SwaineRational Custom, 52: 3 DUKE L.J. 559(2002); Pierre-Hugues Verdier, Cooperative States International Relations, State Responsibility and the Problem of custom, 42 VA L REV 839(2002) he leading article here is goldsmith posner 1999, supra note 2. pcc "self-interest "we mean merely to refer to maximization of preferences--these rences could be other-regarding or altruistic See the cautions expressed in Goldsmith Posner 1999, supra note 2, and the broader treatment in Duncan Nidal, The Game Theory of International Politics, in Kenneth A Oye, ed. COOPERATION UNDER ANARCHY (1986)The Customary International Law Supergame February 23, 2004 2 This article refines and extends an emerging rationalist understanding of CIL. 2 Pioneering work in this field, notably that of Jack Goldsmith and Eric Posner, has begun to articulate a rationalist theory of CIL. Goldsmith and Posner have argued that CIL (a) does not exogenously affect state behavior and (b) is internally incoherent, as states are not motivated by opinio juris to comply with CIL. 3 We show why the first assertion is either tautological or incorrect as a matter of theory, and, to the extent that it purports to rely on factual observation, is not supported by the data presented. The tautology arises from a false dichotomy between motivation by self-interest 4 and motivation by law. In a rationalist model, behavior is assumed to be motivated by self-interest. If law is artificially separated from self-interest, then of course a rationalist model would assume that law has no motivating force. Yet we show how CIL rules may modify the payoffs of behavior and therefore affect behavior through self-interest. While CIL is endogenous to states as a group, it is an exogenous influence on the behavior of each individual state. CIL may affect behavior even if it only does so at the margins. As to the second assertion, our analysis provides a plausible basis to assign a discriminating role to opinio juris, and therefore we find CIL doctrine internally coherent in at least its core dimension. This article develops an iterated multi-player prisoner’s dilemma model of CIL. Of course, game theory can only provide a crude representation of highly nuanced decision-making. 5 Our analysis focuses on parameters of the multi-player prisoner’s dilemma in the CIL context: (i) the relative value of cooperation versus defection, (ii) the number of states effectively involved, (iii) the extent to which increasing the number of 2 See, e.g., Mark A. Chinen, Afterword, 23 MICH. J. INT'L L. 201 (2001); Mark A. Chinen, Game Theory and Customary International Law: A Response to Professors Goldsmith and Posner, 23 MICH. J. INT'L L. 143 (2001); Vincy Fon & Francesco Parisi, International Customary Law and Articulation Theories: An Economic Analysis, George Mason Law and Economics Research Paper No. 02-24, available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=335220; Jack L. Goldsmith & Eric A. Posner, Further Thoughts on Customary International Law, 23 MICH. J. INT'L L. 191 (2001); Jack L. Goldsmith & Eric A. Posner, A Theory of Customary International Law, 66 U. CHI. L. REV. 1113 (1999) [hereinafter Goldsmith & Posner 1999]; Andrew T. Guzman, A Compliance-Based Theory of International Law, 90 CAL. L. REV. 1823 (2002); Francesco Parisi, The Formation of Customary Law, George Mason Law and Economics Research Paper No. 01-06, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=262032; Edward T. Swaine, Rational Custom, 52:3 DUKE L.J. 559 (2002); Pierre-Hugues Verdier, Cooperative States: International Relations, State Responsibility and the Problem of Custom, 42 VA. L. REV. 839 (2002). 3 The leading article here is Goldsmith & Posner 1999, supra note 2. 4 By “self-interest” we mean merely to refer to maximization of preferences—these preferences could be other-regarding or altruistic. 5 See the cautions expressed in Goldsmith & Posner 1999, supra note 2, and the broader treatment in Duncan Snidal, The Game Theory of International Politics, in Kenneth A. Oye, ed., COOPERATION UNDER ANARCHY (1986)