The Customary International Law Supergame February 23, 2004 (1) Defection by state i against state j leads to punishment of i only by state j bilateral defection leads to bilateral punishment;or (ii) Defection by state i against state j leads to punishment of i by all states: bilateral defection leads to multilateral punishment. We focus our analysis on(i)for three reasons. First, it makes the analysis simpler without changing any of the qualitative conclusions. Second, multilateral retaliation ply increases the incentives to comply over bilateral retaliation. Since (i) involves milder punishment of defection than(ii), the conditions that support cooperation with bilateral punishment under(i)will certainly support cooperation with multilater punishment under(ii). In other words, where multilateral punishment is possible, the conditions that we identify below are sufficient but not necessary to support a multilateral rule: any discount factor that supports a multilateral Cil rule with bilateral punishment will also support such a rule with multilateral punishment. Third, there is some force to the argument that (i) is a more plausible scenario than(ii) in most of the situations in which the formulation of Cil is likely to be considered. Articles 42, 48 and 54 of the International Law Commissions Rules on State Responsibility generally prevent retaliation by third states for truly bilateral injury, while there seems no basis for retaliation by an injured state against non-injuring states. These rules seem to limit the formal possibility for multilateral sanctions against truly bilateral defection Thus, in our model, we assume that retaliation is applied bilaterally--that if state defects vis-a-vis state j, only state will respond, and only against state i. If multiple states responded against state i, it would simply make cooperation more likely by increasing the punishment for defection Given (1), we can represent a multilateral prisoner's dilemma game as a set of bilateral games, with a typical bilateral game being as specified in Table l(page 29). As will be seen below, this is not the same as assuming a bilateral game. Rather, it is a multilateral game with bilateral punishment ii. Tit-for-Tat Under"tit-for-tat, states may respond to defection with a single defection. Tit- for-tat is one of the most frequently-discussed strategies in connection with iterated prisoners dilemmas. While tit-for-tat may win evolutionary games, it is not subgame Articles on Responsibility of States for Internationally Wrongful Acts, in Report of the International Law Commission on the Work of Its Fifty-third Session, UN GAOR 56th Sess., Supp. No 10, at 43, UN DoC. A/56/10(2001), available at <www.un.org/law/ilc>,subsequentlynotedbythegeneralAssemblyinA/res/56/83, Responsibility of States for Internationally Wrongful Acts, adopted 12 Dec 2001. These articles do not themselves represent international law, but are an attempt to codify existing custom. See roBert AXelrod, THE EvoLUtIoN OF COOPERATION (1984)The Customary International Law Supergame February 23, 2004 14 (i) Defection by state i against state j leads to punishment of i only by state j: bilateral defection leads to bilateral punishment; or (ii) Defection by state i against state j leads to punishment of i by all states: bilateral defection leads to multilateral punishment. We focus our analysis on (i) for three reasons. First, it makes the analysis simpler without changing any of the qualitative conclusions. Second, multilateral retaliation simply increases the incentives to comply over bilateral retaliation. Since (i) involves milder punishment of defection than (ii), the conditions that support cooperation with bilateral punishment under (i) will certainly support cooperation with multilateral punishment under (ii). In other words, where multilateral punishment is possible, the conditions that we identify below are sufficient but not necessary to support a multilateral rule: any discount factor that supports a multilateral CIL rule with bilateral punishment will also support such a rule with multilateral punishment. Third, there is some force to the argument that (i) is a more plausible scenario than (ii) in most of the situations in which the formulation of CIL is likely to be considered. Articles 42, 48 and 54 of the International Law Commission’s Rules on State Responsibility 40 generally prevent retaliation by third states for truly bilateral injury, while there seems no basis for retaliation by an injured state against non-injuring states. These rules seem to limit the formal possibility for multilateral sanctions against truly bilateral defection. Thus, in our model, we assume that retaliation is applied bilaterally—that if state i defects vis-à-vis state j, only state j will respond, and only against state i. If multiple states responded against state i, it would simply make cooperation more likely by increasing the punishment for defection. Given (i), we can represent a multilateral prisoner’s dilemma game as a set of bilateral games, with a typical bilateral game being as specified in Table 1 (page 29). As will be seen below, this is not the same as assuming a bilateral game. Rather, it is a multilateral game with bilateral punishment. ii. Tit-for-Tat Under “tit-for-tat,” states may respond to defection with a single defection. Tit￾for-tat is one of the most frequently-discussed strategies in connection with iterated prisoner’s dilemmas. While tit-for-tat may win evolutionary games, 41 it is not subgame 40 Articles on Responsibility of States for Internationally Wrongful Acts, in Report of the International Law Commission on the Work of Its Fifty-third Session, UN GAOR, 56th Sess., Supp. No. 10, at 43, UN Doc. A/56/10 (2001), available at <www.un.org/law/ilc>, subsequently noted by the General Assembly in A/RES/56/83, Responsibility of States for Internationally Wrongful Acts, adopted 12 Dec. 2001. These articles do not themselves represent international law, but are an attempt to codify existing custom. 41 See ROBERT AXELROD, THE EVOLUTION OF COOPERATION (1984)