The Customary Internatonal Law Game George Norman * Joel P. Trachtman ** Abstract Structural realsts n poltcal scence and some ratonalst legal scholars argue that customary nternatonal law cannot affect state behavor: that t s epphenomenal. Ths artcle develops a game theoretc model of a multlateral prsoner s dlemma n the customary nternatonal law context that shows that t s plausble that states would comply wth customary nternatonal law under certan crcumstances. Our model shows that these crcumstances relate to: () the relatve value of cooperaton versus defecton, () the number of states effectvely nvolved, () the extent to whch ncreasng the number of states nvolved ncreases the value of cooperaton or the detrments of defecton, ncludng whether the partcular ssue has characterstcs of a commons problem, a publc good, or a network good, (v) the nformaton avalable to the states nvolved regardng complance and defecton, (v) the relatve patence of states n valung the benefts of long-term cooperaton compared to short-term defecton, (v) the expected duraton of nteracton, (v) the frequency of nteracton, and (v) whether there are also blateral relatonshps or other multlateral relatonshps between the nvolved states. Ths model shows that customary nternatonal law s plausble n the sense that t may well affect state behavor where certan condtons are met. It shows what types of contexts, ncludng malleable nsttutonal features, may affect the ablty of states to produce and comply wth customary nternatonal law. Ths artcle dentfes a number of emprcal strateges that may be used to test the model. * Wllam and Joyce Cummngs Famly Char of Entrepreneurshp and Busness Economcs, Tufts Unversty. ** Professor of Internatonal Law, The Fletcher School of Law and Dplomacy, Tufts Unversty. The authors express apprecaton to those who made suggestons or commented on earler drafts, ncludng Kenneth Abbott, Jose Alvarez, Lucan Bebchuk, Davd Bederman, Tomer Broude, Marc Busch, Jeffrey Dunoff, Mchael Glennon, Ryan Goodman, Larry Helfer, Moshe Hrsch, Robert Hockett, Ian Johnstone, Lous Kaplow, Patrck Kelly, Davd Kennedy, Barbara Koremenos, Lsa Martn, Sean Murphy, Phlp Nchols, Erc Posner, Mark Ramseyer, Kal Raustala, Alfred Rubn, Steven Shavell, Beth Smmons, Peter Spro, Rchard Stenberg, Paul Stephan, Edward Swane, Detlev Vagts, sx anonymous referees and partcpants n semnars where earler versons of ths artcle were presented, at Harvard Law School, Hebrew Unversty, the Max Planck Insttute for Comparatve Publc Law and Internatonal Law, UCLA Law School and the Wharton School. We also thank Alexander Gazs and Chrstne Makor for research assstance. Errors are ours.
1. Introducton Customary nternatonal law (CIL) s under attack as behavorally epphenomenal and doctrnally ncoherent. By contrast, the central argument of ths artcle s that CIL, whle somethng of a feat of levtaton, s theoretcally plausble n the sense that t may well affect state behavor n certan crcumstances. CIL s a feat of levtaton nsofar as t rests not on a rock-sold natural law bass of dvne prncples, but on a fabrc of ratonal acts, woven through a multplcty of relatons over tme. Our argument makes one central clam: that whle there are lmts on and varatons n the effectveness of CIL, there are crcumstances where t may ndependently affect the behavor of states. There s no reason n theory, or n data adduced by others, to beleve CIL generally epphenomenal. As CIL s the foundaton of all nternatonal law, ths artcle suggests the crcumstances under whch we would expect nternatonal law to affect state behavor. Ths artcle refnes and extends an emergng ratonalst understandng of CIL. 1 Poneerng work n ths feld, notably that of Jack Goldsmth and Erc Posner, has begun to artculate a ratonalst theory of CIL. Goldsmth and Posner have argued that CIL does not affect state behavor. 2 We show why ths asserton s ether tautologcal or ncorrect as a matter of theory, and, to the extent that t purports to rely on factual observaton, s not supported by the data presented. 3 We construct a more complete model that shows that Goldsmth and Posner s assumpton that the multlateral prsoner s dlemma s unlkely to allow CIL to affect state behavor s false. The tautology of the Goldsmth-Posner argument arses from a false dchotomy between motvaton by self-nterest 4 and motvaton by law. In a ratonalst model, behavor s assumed to be motvated by self-nterest. If law s artfcally separated from self-nterest, then of course a ratonalst model would assume that law has no motvatng force. Yet we show how CIL rules may modfy the payoffs assocated wth relevant behavor, and thereby affect behavor through self-nterest. CIL may affect behavor, 1 See, e.g., Mark A. Chnen, Afterword, 23 MICH. J. INT'L L. 201 (2001); Mark A. Chnen, Game Theory and Customary Internatonal Law: A Response to Professors Goldsmth and Posner, 23 MICH. J. INT'L L. 143 (2001); Vncy Fon & Francesco Pars, Internatonal Customary Law and Artculaton Theores: An Economc Analyss, George Mason Law and Economcs Research Paper No. 02-24, avalable at http://papers.ssrn.com/sol3/papers.cfm?abstract_d=335220; Jack L. Goldsmth & Erc A. Posner, Further Thoughts on Customary Internatonal Law, 23 MICH. J. INT'L L. 191 (2001); Jack L. Goldsmth & Erc A. Posner, A Theory of Customary Internatonal Law, 66 U. CHI. L. REV. 1113 (1999) [herenafter Goldsmth & Posner 1999]; Andrew T. Guzman, A Complance-Based Theory of Internatonal Law, 90 CAL. L. REV. 1823 (2002); Francesco Pars, The Formaton of Customary Law, George Mason Law and Economcs Research Paper No. 01-06, http://papers.ssrn.com/sol3/papers.cfm?abstract_d=262032; Edward T. Swane, Ratonal Custom, 52:3 DUKE L.J. 559 (2002); Perre-Hugues Verder, Cooperatve States: Internatonal Relatons, State Responsblty and the Problem of Custom, 42 VA. L. REV. 839 (2002). 2 The leadng artcle here s Goldsmth & Posner 1999, supra note 1. For a self-descrbed tradtonalst s response, see Detlev F. Vagts, Internatonal Relatons Looks at Customary Internatonal Law: A Tradtonalst s Defence, 15 EUR. J. INT L L. 1031 (2004). 3 See Vagts, supra note 2 (crtqung the use of examples by Goldsmth & Posner). 4 By self-nterest we mean merely to refer to maxmzaton of preferences these preferences could be other-regardng or altrustc.
even f t only does so at the margns. Whle CIL s endogenous to states as a group, meanng that t s not a vertcal structure produced outsde or above the group of states, t s an ndependent (exogenous) nfluence on the behavor of each ndvdual state. Goldsmth and Posner also assert that CIL s nternally ncoherent, as states are not motvated by opno jurs to comply wth CIL. However, our analyss provdes a plausble bass to assgn a dscrmnatng role to opno jurs, and therefore we fnd CIL doctrne nternally coherent n at least ts core dmenson. We understand opno jurs as a way of referrng to the ntent of states to propose or accept a rule of law that wll serve as the focal pont of behavor, wll mplcate an mportant set of default rules that are applcable to law and not to other types of socal order, and that wll mplcate an mportant set of lnkages among legal rules. Ths artcle develops a repeated multlateral 5 prsoner s dlemma 6 model of CIL. Of course, game theory can never capture all real-world detal wth ts hghly nuanced decson-makng. 7 The purpose of game-theoretc models s not to predct or prescrbe behavor, but to generate testable hypotheses that, once tested, are expected to tell us somethng useful about the world. 8 Our analyss focuses on the parameters of the multlateral prsoner s dlemma n the CIL context. These parameters nclude: () the relatve value of cooperaton versus defecton, () the number of states effectvely nvolved, () the extent to whch ncreasng the number of states nvolved ncreases the value of cooperaton or the detrments of defecton, ncludng whether the partcular ssue has characterstcs of a commons problem, a publc good, or a network good, 9 (v) the nformaton avalable to the states nvolved regardng complance and defecton, (v) the relatve patence of states n valung the benefts of long-term cooperaton compared to short-term defecton, (v) the expected duraton of nteracton, (v) the frequency of nteracton, and (v) whether there are also blateral relatonshps or other multlateral relatonshps between the nvolved states. 5 In ths context, we use the term multlateral to refer to contexts n whch more than two partes are nvolved. A more techncal term would be n-person. 6 The prsoner s dlemma s a form of game commonly used n socal scence analyss. In ths artcle, t serves as a vehcle for provdng a formalzed analogy to the CIL context. The structure and assumptons that characterze the prsoner s dlemma are descrbed n parts 2 and 3 below. 7 See the cautons expressed n Goldsmth & Posner 1999, supra note 1, and the broader treatment n Duncan Sndal, The Game Theory of Internatonal Poltcs, n Kenneth A. Oye, ed., COOPERATION UNDER ANARCHY (1986). 8 Whle t may be argued that the game theory that we use, ntally developed n the context of analyss of ndvdual behavor, cannot be appled to state behavor, t should be noted that game theory has been appled to behavor of frms, as well as states. For an argument regardng the adaptaton of these types of models to nternatonal law, see Jeffrey L. Dunoff & Joel P. Trachtman, The Law and Economcs of Internatonal Law, 24 YALE J. INT L L. 1 (1999). 9 Commons problems are crcumstances where persons share a partcular resource, and one person s use of the resource may reduce the amount of the resource avalable to others, whle conservaton of the resource may ncrease the amount of the resource avalable to all. A fshery may present a commons problem n ths sense. Publc goods are goods that are avalable to all, where one person s use of the good does not dmnsh ts avalablty to others. Networks n ths context nvolve crcumstances where wder use of the same good makes the good more valuable to all. Standards often have ths characterstc.
The parameters we dentfy are ncorporated n our model as ndependent varables, but from a normatve standpont t s possble for polcy ntatves to select or manpulate these parameters. That s, by dentfyng the parameters for determnng whether CIL wll affect state behavor, ths artcle opens the way to normatve nsttutonal desgn. States may determne to restructure certan nsttutons n order to facltate the formaton and operaton of CIL. There may be crcumstances under whch t wll be normatvely attractve to facltate the development of CIL, rather than to engage n more self-conscous and statc treaty-makng. The nsttutonal dynamsm and socal mmanence that make socal norms attractve n the domestc context may also be attractve n at least some nternatonal contexts. Ths artcle s organzed as follows. The remander of ths ntroducton provdes a short doctrnal revew of CIL and brefly locates ths artcle n relaton to four lteratures: law and economcs, socal norms, nternatonal organzaton and ndustral organzaton. Our model s largely based on earler work n these areas. Part 2 explans our choce of the repeated multlateral prsoner s dlemma as the bass for our model, as well as our choce of an assumed strategy for players wthn ths model. Any game theory model depends on decsons to assume certan game structures and strateges. We explan here why the prsoner s dlemma game provdes a good ft for the CIL context, and how we choose an assumed strategy for states to follow. Part 3 explans the other assumptons and parameters of our model. Part 4 sets forth four llustratve examples of CIL contexts that mght be understood n terms of our model. Part 5 sets forth the general structure and mplcatons of our model, whle Appendx I sets forth the formal model. Part 6 presents some mplcatons of ths artcle. Part 7 brefly concludes. In bref, ths artcle has mportant mplcatons regardng the plausblty of CIL, the possblty of nsttutonal change to facltate CIL n partcular areas, our understandng of CIL doctrne, and future research n CIL. On the bass of a complete ratonalst model, artculated n formal terms n Appendx I, we show the parameters that wll determne states complance wth CIL. These parameters nclude especally () the relatve patence of ndvdual states to wat for the benefts of recprocal complance by other states, () the mportance of the frequency of nteracton and of the duraton of nteracton n order to ncrease the potental value of future recprocal benefts, () the possblty that complance n one settng may be supported by overlappng relatonshps n other settngs, (v) the structure of the benefts from cooperaton, ncludng whether benefts may ncrease or decrease wth the number of states that cooperate. Based on ths understandng, states may create nsttutonal responses n order to enhance the possbltes of complance wth partcular rules of CIL. But CIL s not merely a label for ratonal cooperaton. Rather, CIL s a specal branch of cooperaton that has partcular features. These features nclude the establshment of a focal pont so that states may readly dentfy what wll count as cooperaton, attenton to the motvaton of states to offer and accept a rule of law (opno jurs), wth certan default rules and prescrbed consequences, and the lnkage of the partcular rule wth the broader nternatonal legal system. In ths last regard, we mght
say that by ncludng a partcular rule n CIL, states are acceptng that the rest of the legal system s hostage to complance wth the partcular rule. Ths adds strong ncentves for complance. Yet ths s only the begnnng of a ratonalst research program n CIL. Theory such as the one artculated n ths artcle must be tested and refned based on emprcal observaton. By artculatng a set of parameters for determnng the lkelhood of complance, ths artcle also suggests the contours of a broader research program n CIL. a. Customary Internatonal Law and ts Doctrne As an ntroductory matter, t s useful to revew the fundamental doctrne of CIL. Artcle 38(1)(b) of the Statute of the Internatonal Court of Justce, lstng the sources of nternatonal law applcable by the Court, ncludes nternatonal custom, as evdence of a general practce accepted as law. Artcle 102 of the Amercan Law Insttute s Restatement (Thrd) of Foregn Relatons Law states that [c]ustomary nternatonal law results from a general and consstent practce of states followed by them from a sense of legal oblgaton. The sense of oblgaton s referred to n Latn as opno jurs sve necesstats. CIL has two core doctrnal problems relatng to opno jurs. Frst, can CIL ever come nto exstence f t requres opno jurs a sense of legal oblgaton before t can exst? The second, related, problem relates to the motvaton of states. Are states ever motvated by opno jurs? The ratonalst assumpton that states are motvated by ther own preferences seems prma face nconsstent wth the CIL requrement of motvaton by opno jurs, and ths s the crtcsm that Goldsmth and Posner level at CIL doctrne. 10 They argue that what appears to be CIL s not, because t s actually motvated by concdence of nterest, coercon, cooperaton predcated on self-nterest, or coordnaton predcated on self-nterest. We respond to ths argument n part 6. As suggested above, for the socal scentst studyng law, the crtcal descrptve queston relates to the effects of legal rules on behavor. For CIL, ths descrptve queston s also a doctrnal queston, as CIL doctrne requres some level of generalty and consstency of practce some quantum of state behavor. And agan, at least under the Restatement formulaton, ths behavor must be motvated by opno jurs. Under the Statute of the Internatonal Court of Justce, the custom tself may serve as evdence of acceptance as law, of opno jurs. Some commentators have suggested that opno jurs n a formal sense may not be necessary at all, but that the requrement should be understood n terms of state consent or acceptance. 11 As we address the theory of CIL, t s useful to have n mnd some examples of CIL. CIL exsts n a wde varety of felds, and coexsts n many areas wth treaty law. As already noted, CIL s ts own foundaton. Thus, there s a CIL of CIL. In other words, the CIL doctrne dscussed above s understood as law pursuant to CIL. 10 11 Goldsmth & Posner 1999, supra note 1. Maurce H. Mendelson, The Formaton of Customary Internatonal Law, 272 RECUEIL DES COURS 155, 268-293 (1998).
Furthermore, the law of treates came nto exstence pursuant to CIL, although ths law s today codfed n treaty. But movng beyond these foundatonal areas, CIL addresses, for example, ssues of terrtoral ntegrty, jursdcton to apply law, dplomatc mmunty, the rghts of states wth respect to coastal areas, human rghts, cross-border polluton and the use of force to settle nternatonal dsputes. These are dverse felds, each wth ts own characterstcs. Our theoretcal approach calls for dscrmnaton among these felds: not all CIL s created equal. Not all law s equally or peremptorly bndng. Our model ndcates the parameters for dscrmnaton. Smply put, we would expect greater possblty for formaton of and complance wth CIL n some felds than n others. Of course, ths s an area n whch emprcsm would requre analyss of areas n whch CIL has not developed: the dog that dd not bark. Thus, we mght ask, why s there no CIL rule that requres extradton of crmnals? Our theoretcal approach also accepts the possblty of lnkage among dverse felds, ntegratng and therefore homogenzng the behavoral effect of each rule of law. b. Four Lteratures Ths artcle draws on four sem-autonomous lteratures. Frst, as noted above, there s an emergng ratonalst, law and economcs-based lterature of CIL. The leadng work n ths area s by Goldsmth and Posner, but there are other mportant contrbutons. Second, ths artcle draws on a burgeonng lterature on socal norms n the law, although socal norms are studed by all manner of socal scentsts. Thrd, ths artcle draws on the economcs feld of ndustral organzaton for game theory-based nsghts about colluson among compettors n markets. Fourth, ths artcle draws on the poltcal scence lterature of nternatonal organzaton, whch has addressed n detal the game theoretc analyss of cooperaton among groups of states.. Law and Economcs of CIL Goldsmth and Posner provde a game theoretc analyss of CIL. They examne a varety of CIL crcumstances, and argue that these crcumstances can be categorzed nto four game types: () concdence of nterest, () coercon, () blateral cooperaton, and (v) blateral coordnaton. Ths s a useful exercse, as t nvtes us to consder the motvaton of states, and the degree to whch CIL affects behavor. In the perhaps hypothetcal cases of pure concdence of nterest and pure coercon, Goldsmth and Posner are correct that there can be no opno jurs, and that law does lttle work. Ths s not new to CIL doctrne, but t s useful to emphasze. It s also worth notng that Goldsmth and Posner seem to assume a purty of motvaton that may not exst n the real world. Goldsmth and Posner suggest that many nstances of observed CIL may be understood n terms of blateral cooperaton along the lnes of a blateral prsoner s dlemma game. They then argue that Although game theory does not rule out the
possblty of n-state cooperaton, the assumptons requred for such an outcome are qute strong and usually unrealstc. For ths reason, we doubt the utlty of n-player prsoner's dlemmas as an explanaton for multlateral or unversal behavoral regulartes. 12 Ther vews wth respect to coordnaton games are smlar. The present artcle shows that the assumptons for multlateral or n-state cooperaton are nether strong nor unrealstc, but are n some cases qute plausble. In addton to developng ths theoretcal perspectve, Goldsmth and Posner examne several examples of CIL. The areas they consder are neutralty, dplomatc mmunty and martme jursdcton. They beleve that n these areas, states were motvated by concdence of nterest, coercon or a blateral recprocty along the lnes of the prsoner s dlemma. They conclude that f state behavor can be explaned by concdence of nterest or coercon, or any other self-nterested-motvaton, then nether opno jurs nor CIL does any motvatonal work.. Socal Norms We mght ask, however, whether the CIL problem s dfferent n structure from the socal norms context, and whether f socal norms can affect behavor, CIL can as well. Snce the publcaton by Robert Ellckson of Order Wthout Law 13 n 1991, legal scholars have examned the role of nformal norms n socety, and the relatonshp of these norms to law. Ellckson nvestgates how cattle farmers n Shasta County, Calforna, manage to establsh and apply ther own non-legal rules, wth a notable level of complance, wthout drect nterventon by the state. It s an nsghtful story about how order can arse wthout law, or n spte of law. 14 We may draw a rough, and lmted, analogy between the development of socal norms n a muncpal, or prvate settng, 15 and the development of CIL n the nternatonal publc settng. In the nternatonal communty, CIL s substantvely smlar to the phenomenon Ellckson descrbes. 16 In nternatonal poltcal scence, regme theorsts such as Robert Keohane, 17 Stephen Krasner, and Beth Smmons 18 have told a smlar story of the possble rse of order n nternatonal socety. However, regme theory has 12 13 14 Goldsmth & Posner 1999, supra note 1, at 1130. ROBERT ELLICKSON, ORDER WITHOUT LAW (1991). However, one mght argue that the general legal system, ncludng especally ts rules aganst volence, forms an mportant background or nfrastructure that may provde support to the farmers' socal norms. 15 For a recent work syntheszng and extendng some of the socal norms learnng, see ERIC A. POSNER, LAW AND SOCIAL NORMS (2000). See also Rchard H. McAdams, Book Revew: Sgnalng Dscount Rates: Law, Norms and Economc Methodology, 110 YALE L.J. 625 (2001). 16 For an example of ths type of analogcal allegory, comparng domestc custom to nternatonal custom, see Mendelson, supra note 11, at 165-168. For an early statement that CIL s produced n an evolutonary fashon, see ANTHONY A. D'AMATO, THE CONCEPT OF CUSTOM IN INTERNATIONAL LAW 104 (Cornell 1971). 17 See, e.g., ROBERT O. KEOHANE, AFTER HEGEMONY: COOPERATION AND DISCORD IN THE WORLD POLITICAL ECONOMY (1984); ROBERT O. KEOHANE, INTERNATIONAL INSTITUTIONS AND STATE POWER: ESSAY IN INTERNATIONAL RELATIONS THEORY (1989). 18 See, e.g., STEPHEN D. KRASNER, INTERNATIONAL REGIMES (1983); Stephen D. Krasner & Beth Smmons, Theores of Internatonal Regmes, 41 INT L ORG. 491 (1987).
generally avoded CIL. 19 Moreover, recognton that a rule has become part of CIL may sgnal ts support by, or lnkage wth, the mult-sector nternatonal legal system. Ths system of accepted and enforced lnkage may dstngush legal rules from non-legal regmes. The dfference between law and socal norms n the muncpal settng s that law s the provnce of the state (settng asde for the moment relgous law, other non-state rules, and crcumstances n whch non-state made rules are ncorporated n the stateenforced law). 20 However, ths dstncton s napposte to the nternatonal system, whch has been characterzed as a horzontal, as opposed to vertcal, system, where there s no overarchng state, per se. 21 So, n the nternatonal system, there s more overlap, and an ndstnct border, between law and socal norms. Ths overlap s perhaps easer to see n the nternatonal context than n the domestc context, as, n the nternatonal context, a sgnfcant subset of socal norms s termed "law." Ellckson states that the socal norms lterature defnes a socal norm as a rule governng an ndvdual s behavor that thrd partes other than state agents dffusely enforce by means of socal sanctons. 22 The focus of ths defnton on decentralzed means of enforcement shows the strong analogy between socal norms n the muncpal settng and CIL n the nternatonal settng. Of course, to the extent that nternatonal courts may apply, and nsttutons of global governance may enforce, CIL, there s a dfference. But ths applcaton and enforceablty s qute lmted. There are few crcumstances n whch CIL rules beneft from mandatory adjudcaton n nternatonal trbunals. We would not consder applcaton of CIL by domestc courts to amount to the acton of state agents at the nternatonal level, although acton by domestc courts would certanly be consdered acton of state agents at the muncpal level. Ths s because n the nternatonal context, domestc courts are smply nternal delberatve processes of natonal governments. The applcaton by domestc courts of CIL may be understood as a knd of norm nternalzaton. 23 19 Duncan Sndal, Poltcal Economy and Internatonal Insttutons, 16 INT'L REV. L. & ECON. 121, 124 (1996). 20 Whle there s no state at the global level, there s an nternatonal legal and organzatonal order, whch s qute a bt more fragmented than most naton-states. 21 We add ths qualfcaton, because one mght argue that the CIL and conventonal law framework, as t exsts, s at least comparable to a muncpal state, or at least that ths framework s comparable to the consttuton that a muncpal state mght have. Of course, whle t responds to some of the same questons, ncludng a rule of recognton, t s not as detaled or fertle as a consttuton. 22 Robert Ellckson, The Evoluton of Socal Norms: A Perspectve from the Legal Academy, n SOCIAL NORMS 35 (Mchael Hechter & Karl-Deter Opp eds., 2001). Note that Ellckson assumes multlateral, as opposed to blateral, retalaton. 23 See Harold Hongju Koh, Why Do Natons Obey Internatonal Law?, 106 YALE L.J. 2599 (1997) (revewng Abram Chayes & Antona Handler Chayes, THE NEW SOVEREIGNTY: COMPLIANCE WITH INTERNATIONAL REGULATORY AGREEMENTS (1995)). Ths nternalzaton may be desrable under certan crcumstances, and may be developed as a tool of enforcement of CIL. That s, states may persuade one another to harness ther domestc legal system for certan of ther nternatonal legal oblgatons, effectvely holdng the domestc legal system hostage. See also Phlp Moremen & Joel P. Trachtman, Whose Rght s t Anyway? Prvate Partes n EC-U.S. Dspute Settlement at the WTO, 44 HARV. INT L L. J. 221 (2003).
One mportant set of explanatons of socal norms understands norms as preferences that ndvduals (or n our case states) acqure through educaton, acculturaton or other processes, such as an expressve or artculaton functon. 24 It may well be possble to modfy preferences of states through socal norms. It seems obvous that the way to modfy the preferences of states s to modfy the preferences of ndvdual government offcals, or voters. Indeed, t may be approprate to consder epstemc communtes and networks among government offcals as channels of preferencemodfcaton. Whle ths approach may have tracton n the CIL settng, and may reemphasze the role of arguments predcated on legtmacy, justce and moralty as bases for preference-modfcaton, ths artcle wll bypass that dscusson, and focus on exogenous explanatons of socal norms, that s, explanatons that look at external nfluences on actors, rather than nternal changes n actors. 25 Modelng always nvolves smplfcaton, and our goal n ths artcle s to elaborate a ratonalst model for future testng. In fact, testng an exogenous model would help to advance the debate between exogenous and endogenous causes of complance wth CIL. In connecton wth exogenous explanatons, the law-based socal norms lterature has not embraced the repeated multlateral prsoner s dlemma. 26 Ths s due to two types of concerns. Frst, there are concerns that game theory does not reflect the nuance of socal nteracton. We hope that the ncorporaton n our model of mult-sector contact helps to address ths concern. Second, there are concerns regardng the credblty of thrd-party enforcement. 27 Wll thrd partes be properly motvated to jon n retalaton aganst volators? If the threat of retalaton s not credble, there wll be strong ncentves for volaton. We address these concerns below.. Industral Organzaton Much of our understandng of the utlty, structure and dynamcs of multlateral prsoner s dlemma games comes from the economcs lterature of ndustral organzaton. Ths lterature consders the possblty that frms may enter nto cartels or other restrctons of competton that volate anttrust laws. Whle frms may fnd opportuntes to communcate, ther communcatons and agreements must be kept secret from the regulatory authortes and are not enforceable at law. Ths legal restrant on the enforcement of agreements s analogous to the lmtaton n the nternatonal law settng on enforcement of agreements. An mportant concern for ndustral organzaton 24 25 See Robert D. Cooter, Expressve Law and Economcs, 27 J. LEG. STUDS. 585 (1998). Robert D. Cooter, Do Good Laws Make Good Ctzens? An Economc Analyss of Internalzed Norms, 86 VA. L. REV. 1577 (2000); Robert C. Cooter, Models of Moralty n Law and Economcs: Self-Control and Self-Improvement for the Bad Man of Holmes, 78 B.U. L. REV. 903, 911-912 (1998); JON ELSTER, THE CEMENT OF SOCIETY: A STUDY OF SOCIAL ORDER (1989). Basu refers to these as preferencechangng norms. See Kaushk Basu, Socal Norms and the Law, 3 THE NEW PALGRAVE DICTIONARY OF ECONOMICS AND THE LAW 476 (1998). 26 See Paul G. Mahoney & Chrs Wllam Sanchrco, Norms, Repeated Games, and the Role of Law, 91 CAL. L. REV. 1281, 1284 (2003). Mahoney and Sanchrco explan the state of the socal norms lterature wth respect to the multlateral prsoner s dlemma. They explan that the objecton to these models s that thrd party enforcement s not ndvdually ratonal: that the players lack ncentves to retalate. 27 Id. at note 12, ctng work by Ellckson, Katz, McAdams and Posner.
economsts s to dentfy crcumstances under whch agreements can be made selfsustanng through the self-nterest of the partes to the agreement. Whle the analogy s apparent, we must recognze, of course, that n the CIL settng, publc communcaton s possble, as are agreements that at least purport to be bndng: treates. The degree to whch agreements may actually constran behavor s a queston for another artcle, but we pont out that the nternatonal legal rule that treates must be observed (pacta sunt servanda) s tself part of CIL. Another, perhaps more mportant, dstncton s that a cartel has certan characterstcs that may dffer from any partcular CIL settng. That s, n a cartel, the more others adhere to the cartel, the greater the monetary ncentves for any partcular member to defect. Ths context s more lke a commons problem than lke a publc good or network problem. We wll dscuss some of these dstnctons based on varatons n payoff structures below. v. Internatonal Organzaton Poltcal scentsts and economsts workng n the feld of nternatonal organzaton have made a good deal of progress n analyzng the problem of nternatonal cooperaton more generally. In varous works, they have examned most of the parameters that we utlze here. 28 Ths lterature has not examned CIL. The model we present here formalzes certan consderatons that reman nformal n much of the poltcal scence lterature, and has other dstnctve features that we descrbe below. We have structured our model to match most closely the CIL context, rather than attempt to structure a model that would address other nternatonal cooperaton devces. However, we recognze that the queston of whch devce treaty, CIL or softer law tself depends on a set of varables. We also recognze that CIL may be understood as a phase n the formalzaton of law, or n legalzaton. 29 The Internatonal Law Commsson of the Unted Natons often codfes CIL, and CIL often forms the bass for treates. Ths artcle does not present an explanaton of choce between custom and treaty, or of the relatonshp among these nstruments. 30 28 There s dsagreement between nsttutonalsts and realsts, who clam that states nterests n nternatonal relatons are characterzed by a search for relatve gans, rather than absolute gans. These realsts reject the possblty of cooperaton where t results n relatve gans to a compettor. See Marc Busch & Erc Renhardt, Nce Strateges n a World of Relatve Gans: The Problem of Cooperaton under Anarchy 37 J. CONFL. RES. 427 (1993); Robert Powell, Absolute and Relatve Gans n Internatonal Relatons Theory, 85 AM. POL. SCI. REV. 1303 (1991); Duncan Sndal, Relatve Gans and the Pattern of Internatonal Cooperaton, 85 AM. POL. SCI. REV. 701 (1991). 29 See the specal ssue of Internatonal Organzaton devoted to the phenomenon of legalzaton. 54:3 INT L ORG. (2000). 30 See Kenneth Abbott & Duncan Sndal, Hard and Soft Law n Internatonal Governance, 54 INT L ORG. (2000); John K. Setear, Treaty, Custom, Iteraton and Publc Choce, February 2004, avalable at http://ssrn.com/abstract=492604 (argung that custom s more attractve to executve branches). To the extent that CIL s less detaled less specfc than treaty norms, t s amenable to a rules versus standards type of analyss. See Lous Kaplow, Rules versus Standards: An Economc Analyss, 42 DUKE L.J. 557,
2. The Multlateral Prsoner s Dlemma Game theory develops models to depct, to abstract, and to formalze, varous socal settngs. Gven the dversty of socal contexts, there s a wde choce of models from whch to choose. 31 In ths secton we explan our choce of the multlateral prsoner s dlemma as the basc model for the CIL problem, examne the potental strateges that mght be played wthn ths game, and explan some of our assumptons. The multlateral repeated prsoner s dlemma s tself really a group of varyng models, wth a number of varyng features, ncludng the number of players and ther preferences. a. Choce of Game The basc payoff structure assumed n the prsoner s dlemma game captures the essental problem of cooperaton n a horzontal socal settng wth externaltes, 32 n whch partes have a choce between complance and defecton, and n whch they can enrch themselves ndvdually through defecton whle they could enrch socety, and n lght of the antcpated actons of others, themselves, through complance. 33 Of course, some CIL contexts mght be better modeled usng other methods, but by usng the prsoner s dlemma we hope to capture the essence of nformal contractng under opposed nterests. 34 One of the reasons that we choose ths game s because t allows us to contextualze a number of nsghts and concerns that cannot easly be ncluded n other analytcal models. For example, we beleve that the multlateral prsoner s dlemma can 577 (1992); Joel P. Trachtman, The Doman of WTO Dspute Resoluton, 40 HARV. INT'L L.J. 333, 346-47 (1999). 31 For a useful analyss of the ft of other games, ncludng battle of the sexes and stag hunt, see Swane, supra note 1. See also Fona McGllvray & Alastar Smth, Trust and Cooperaton Through Agent-Specfc Punshments, 54 INT'L ORG. 809, 810 (2000) (notng that the prsoner s dlemma s often used to model nternatonal cooperaton). 32 By use of the term externaltes, we mean to be qute nclusve, ncludng both pecunary and nonpecunary externaltes: any crcumstance n whch an acton by one state has adverse or benefcal effects on another state. 33 At another level of complexty, t would be possble to model the game of formaton of a CIL rule separately from enforcement. See James D. Fearon, Barganng, Enforcement, and Internatonal Cooperaton, 52:2 INT L. ORG. 269 (1998) (separatng the barganng problem, modeled as a coordnaton game, from the enforcement problem, modeled as a prsoner s dlemma); Stephen D. Krasner, Global Communcatons and Natonal Power: Lfe on the Pareto Fronter, 43 WORLD POL. 336 (1991) (argung that many nternatonal ssues are better modeled as coordnaton games). Fearon s two stage approach may be more approprate to the treaty context than to the custom context. Fearon ponts out that relatvely large shadows of the future mght nhbt barganng to acheve an ntal coordnaton game agreement, whle makng the enforcement game more tractable. In the CIL context, there s less natural separaton, and there may even be frst mover advantages that would counteract the effect Fearon suggests. Fnally, our nterest n ths artcle s not so much n establshng CIL rules, as n enforcng them. 34 For a dscusson of the use of coordnaton games to model certan types of nternatonal contexts, see Barbara Koremenos, Charles Lpson, & Duncan Sndal, The Ratonal Desgn of Internatonal Insttutons, 55:4 INT L ORG. 761, 774 (2001); Duncan Sndal, Coordnaton versus Prsoner s Dlemma: Implcatons for Internatonal Cooperaton and Regmes, 79:4 AM. POL. SCI. REV. 923 (1985).
take account of a number of the dverse consderatons often referred to together as reputaton or reputatonal sanctons. 35 We also beleve that the multlateral prsoner s dlemma must be at the core of a ratonalst explanaton of the effectveness of socal norms. Fnally, we beleve that the multlateral prsoner s dlemma offers parsmony: n the CIL context, the factors that t takes nto account seem necessary, and there are no factors that seem superfluous. The prsoner s dlemma s a non-cooperatve game, meanng that the players are unable to enter nto bndng agreements wth one another. Although treates are bndng n a formal legal sense, as the source of ther bndng force s CIL tself, t seems approprate at the outset to model CIL as a non-cooperatve game. However, t may be approprate to relax the assumpton that the general nternatonal legal context s a noncooperatve game once we determne that the CIL of pacta sunt servanda has bndng force, lendng bndng force to treates. Whle ths s crtcal to treaty law, t should be emphaszed that t does not affect our analyss of CIL. Thus, n a non-cooperatve, sngle-play crcumstance, wth a standard prsoner s dlemma payoff structure, we would expect non-complance. 36 Ths s each player s domnant strategy, meanng that each player s payoff from defecton s superor to ts payoff from cooperaton, no matter what the other player does. Ths domnant strategy s llustrated n the table below, n whch no matter what State B does, State A obtans a better payoff by defectng. 37 Prsoner s Dlemma Game State B Cooperate Defect A State Cooperate 3;3 [sum=6] 1;4 Defect 4;1 2;2 [sum=4] 35 36 37 See Guzman, supra note 1. STEPHEN MARTIN, ADVANCED INDUSTRIAL ECONOMICS 98 (1993). Blateral defecton s a Nash equlbrum because under the payoffs assumed n the prsoner s dlemma, each party s better off defectng, no matter what the other party does. A Nash equlbrum s a set of strateges such that each player s strategy s an optmal response to the other players strateges. DREW FUDENBERG & JEAN TIROLE, GAME THEORY 11 (1991).
Therefore, under the rather restrctve assumptons of the true prsoner s dlemma, the partes each nvarably choose the strategy that results n reduced ndvdual welfare, and reduced aggregate welfare, compared to the non-defectng strategy. Ths s an neffcent outcome. By analogy, states playng the CIL game (assumng prsoner s dlemma-type payoffs) n a blateral sngle-play settng would fal to form or comply wth a CIL rule that ncreased ndvdual and aggregate welfare. Cooperaton s strongly domnated, and the resultng equlbrum s for both states to defect. 38 The same s true of a prsoner s dlemma game repeated a fnte number of tmes known n advance to the players. Agan, the unque resultng equlbrum s for each player to defect n each perod. 39 Ths concluson s nescapable n theory, gven the constrants of the game: by defnton, the outcome of the prsoner s dlemma game s an neffcent strategc equlbrum. Ths concluson presents a normatve goal: to modfy the real world crcumstances so as to produce stable equlbra that are effcent. Ths s the major role of CIL, and of nternatonal law generally. Of course, n a world of effectve thrd-party enforcement of agreements, the response to the prsoner s dlemma s clear: the partes would enter nto a bndng agreement to cooperate, thereby modfyng the payoff structure and escapng the prsoner s dlemma. The prsoner s dlemma assumes, however, that ts prsoners are held separately, and cannot negotate, reach, or enforce a bndng agreement. In the CIL settng, there s no court of general mandatory jursdcton nor any publcly apponted polceman. Whle we may draw analoges to the World Court and the U.N., these nsttutons have substantal dfferences compared to domestc courts and polce. Therefore, we begn by assumng that there s no capacty to make agreements that are bndng. Ths s obvously a smplfyng assumpton. In fact, our model s meant to show that there are substtutes for formal bndng agreements, and that these nformal substtutes may have bndng force. Once the capacty to bnd s establshed, the players are no longer n a prsoner s dlemma. In the CIL game, there are four addtonal mportant dstnctons from the assumptons of non-cooperatve game theory n general, and the prsoner s dlemma n partcular. Frst, the players can communcate wth one another, and can do so more readly today than durng the classcal perod of formaton of CIL. Second, states play a repeated game wth one another wth no defned end date, and so can respond at a later tme to somethng done at an earler tme. Updatng of nformaton and punshment are possble. Thrd, not only s the narrow game characterzed by a partcular CIL rule, lke the three-mle terrtoral sea, but t s embedded n a dense fabrc of relatonshps. Fourth, nformaton regardng complance s often readly accessble; more so today, t would appear, than durng the 19 th century. Each of these dstnctons alone may be suffcent to 38 39 Ths s a Nash equlbrum. Id. at 111. Ths s a subgame perfect equlbrum. A subgame perfect equlbrum s a strategy profle that nduces a Nash equlbrum n every subgame. M.J. OSBORNE, AN INTRODUCTION TO GAME THEORY (Oxford Unversty Press, 2004).
transform the game nto somethng qute dfferent from the prsoner s dlemma whle nothng resolves the true prsoner s dlemma, modfcatons may result n stable and effcent equlbra. Indeed, t may be useful to use cooperatve game theory to analyze some CIL crcumstances. 40 As wll be llustrated below, one of the more dffcult types of multlateral cooperaton problem s a commons problem n whch, as n the cartel context, ncentves to defect ncrease wth the number of other states that comply. The more that the common s protected, the greater the benefts of defectng. Where ncentves to defect ncrease wth the number of players, we would expect the most severe challenge to cooperaton. Not all CIL contexts exhbt ths characterstc. Observaton suggests that even certan commons problems, or other prsoner s dlemma-type crcumstances, may acheve resoluton despte theory. Elnor Ostrom states that [a] substantal gap exsts between the theoretcal predcton that selfnterested ndvduals wll have extreme dffculty n coordnatng collectve acton and the realty that such cooperatve behavor s wdespread, although far from nevtable. 41 Ostrom ctes consderable evdence regardng the amount and crcumstances of cooperaton by ndvduals n multlateral collectve acton problems. The evdence shows that ndvduals contrbute to the resoluton of these problems n substantally greater amounts than the standard prsoner s dlemma model would suggest. Of course, much of the evdence s obtaned n crcumstances where the assumptons of the prsoner s dlemma are volated by allowng ndvduals to communcate, enter nto agreements and repeat play. We do not deploy any statstcally sgnfcant data n ths artcle. However, we advance a plausble theory of potental effcent equlbra n the multlateral prsoner s dlemma, and suggest some possble approaches to emprcal testng. b. Choce of Strategy The next step n constructng our model s to postulate a plausble strategy that states mght play wthn the prsoner s dlemma. There are many choces. We menton three strateges of retalaton derved from the lterature of game theory: tt-for-tat, grm trgger, and penance. These strateges are stylzed assumptons about state behavor, and they are necessary n order to complete the model. However, the reader wll see that these strateges seem lke plausble state responses to defecton by others n partcular crcumstances. There are two ways n whch retalaton mght occur: the harmed state alone retalates (blateral retalaton) or the broader communty of states retalate (multlateral retalaton). In secton 4 below, we dscuss the possblty of blateral or multlateral retalaton, and how ths choce would affect our model. 40 For an applcaton of cooperatve game theory n the nternatonal context, see Danel G. Arce M. & Todd Sandler, A Cooperatve Game Theory of Non-Contguous Alles, 3 J. PUB. ECON. THEORY 391 (2000) (applyng cooperatve game theory to nternatonal securty arrangements). 41 Elnor Ostrom, Collectve Acton and the Evoluton of Socal Norms, 14:3 J. ECON. PERSP. 137, 138 (2000).
. Tt-for-Tat Under tt-for-tat, states may respond to defecton wth a sngle defecton. Ttfor-tat s one of the most frequently-dscussed strateges n connecton wth repeated prsoner s dlemmas. Whle tt-for-tat may wn evolutonary games, 42 t s not credble: after a defecton, the wronged state wll have ncentves to accept an undertakng from the defectng state that t wll cooperate n future. 43 Even more devastatng to tt-for-tat s the fact that once one state defects the game cycles endlessly between defecton and complance. 44 Gven the mplausblty of tt-for-tat, we reject t and do not evaluate the mplcatons of ts use.. Grm Trgger Second, states may respond to a sngle defecton wth defecton forever: a grm trgger strategy. There are two basc approaches that have been developed n the theory of repeated games. The frst assumes that any devaton s met wth a response that maxmzes the loss that the devator suffers a mnmax strategy even f ths mposes costs on the punshers. The second approach assumes that devaton results n reverson to the Nash equlbrum of the prsoner s dlemma game: defecton. We adopt the latter approach snce t appears to be more appealng to players. Essentally, we assume that n the event of devaton the states revert to the strateges that they would have adopted f no CIL rule had developed n the frst place. The grm trgger strategy s credble, as t calls for a reverson to the domnant strategy of defecton n response to an ntal defecton. However, the grm trgger strategy s unappealng for the same reason that falure to resolve the prsoner s dlemma of cooperaton s unappealng: t results n neffcency. 45 Thus, n hs work on treates relatng to envronmental commons problems, 46 Barrett rejects the grm trgger strategy because t fals to satsfy the crteron of collectve ratonalty. The collectve ratonalty consderaton s a formal artculaton of the ntutve concern that t would be extraordnarly wasteful to abandon an effcent multlateral agreement because of a sngle defecton. Whle t would be ndvdually ratonal to respond wth defecton forever t smply calls for reverson to the Nash equlbrum t s collectvely rratonal nsofar as ratonal negotators wll have ncentves to renegotate a cooperatve arrangement after defecton. Therefore, t s not credble. 42 43 See ROBERT AXELROD, THE EVOLUTION OF COOPERATION (1984). In the language of game theory, t s not subgame perfect. Subgame perfecton means that at every stage of a repeated game, no player wll have an ncentve to devate from the equlbrum strategy, even when others do. See note 39, supra. 44 Id., at 138. 45 Goldsmth and Posner appear to recognze the possblty for stable and effcent equlbra under certan crcumstances where states play the grm trgger strategy. However, usng an overfshng of commons context as ther example, they suggest that the grm trgger s not used and would be collectvely rratonal. Goldsmth & Posner 1999, supra note 1, at 1129-1130. 46 Scott Barrett, A Theory of Full Internatonal Cooperaton, 11 J. THEORETICAL POL. 519 (1999); SCOTT BARRETT, ENVIRONMENT AND STATECRAFT: STRATEGIES OF ENVIRONMENTAL TREATY-MAKING (2003).
Wth respect to the more emprcal queston of whether a grm trgger strategy s actually used, f we thnk not about the CIL that exsts, but about the CIL that does not exst, t s clear that states do play the grm trgger strategy at least n some contexts. In fact, one mght argue that the grm trgger s the exstng default strategy n CIL. That s, where a CIL rule exsts or s proposed for formaton, and one state devates, that may be suffcent provocaton to cause others to devate forever n response: to kll the rule multlaterally. The grm trgger strategy s not credble because t s not renegotaton-proof. 47 That s, after a defecton, non-defectng states wll have ncentves to come together and cooperate wth the defector, deprvng the grm trgger of credblty and therefore effectveness. The defector can make an appealng let bygones be bygones argument. 48 An obvous counterargument to ths, of course, s that renegotaton unravels f states perceve that ths argument may be made repeatedly. That s, once the players understand that defecton and promses of future complance wll go on ndefntely, would they not declne to renegotate the frst tme? Moreover, n the CIL context, we are operatng on the assumpton that states do not have the possblty of formng bndng agreements through renegotaton, preventng ths ndefnte defecton. 49 Nevertheless, there may be crcumstances n whch such renegotaton s possble, and the offer to renegotate and abde by the results s credble. If so, states wll have ncentves to defect and an alternatve, renegotaton-proof, strategy s needed. We offer the penance strategy descrbed below as a weakly renegotaton-proof alternatve.. Penance If renegotaton s possble and credble, the states wll prefer to renegotate after a defecton, makng defecton an attractve opton. 50 The strategy known as penance 51, s both ndvdually credble n that states would ndvdually fnd t attractve to play t, and collectvely credble n the sense that t s lkely to be more attractve than 47 See, e.g., Joseph Farrell & Erc Maskn, Renegotaton n Repeated Games, 1 GAMES & ECON. BEHAVIOR (1989); Fudenberg & Trole, supra note 38, at 174. 48 Indeed, ths s not uncommon n nternatonal law dscourse. See, e.g., Scott M. Sullvan, Changng The Premse Of Internatonal Legal Remedes: The Unfounded Adopton Of Assurances And Guarantees Of Non-Repetton, 7 U.C.L.A. J. INT L L. & FOR. AFF. 265 (2002-2003). 49 Barrett notes that collectve ratonalty s less of an ssue n the feld of domestc anttrust law, because renegotaton of an agreement n restrant of trade s llegal. Barrett, supra note 46, at 11. 50 Whle a precse defnton of renegotaton-proofness has not yet been agreed n the game theory lterature, the treatment by Farrell and Maskn s worth consderng. They defne a weakly renegotatonproof (WRP) equlbrum for an nfntely repeated game to be a subgame perfect equlbrum strategy profle that s not Pareto-domnated by any other subgame perfect strategy profle. Usng ths defnton, the grm trgger strategy profle descrbed above s not WRP, snce after defecton the payoffs to cooperaton Pareto-domnate those of punshment. Farrell & Maskn, supra note 47. 51 See Fudenberg & Trole, supra note 38, at 179-182. Penance s sometmes referred to as gettng even. See ROGER B. MYERSON, GAME THEORY: ANALYSIS OF CONFLICT 326-27 (1991).