The Customary International Law Supergame: Order and Law

Transcription

1 13 July 2004 The Customary Internatonal Law Supergame: Order and Law Abstract George Norman * Joel P. Trachtman ** Customary nternatonal law s an engma. It s produced by the decentralzed actons of states, and t generally lacks centralzed enforcement mechansms. Poltcal scence realsts and some ratonalst legal scholars argue that customary nternatonal law cannot affect state behavor: that t s epphenomenal. Ths artcle develops a model of an n-person 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. 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, (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. One mplcaton of ths model s that t lends credence to customary nternatonal law. From a research standpont, ths model dentfes a number of parameters for whch data may be developed n order to test the model. From a polcy standpont, ths model shows what types of contexts, ncludng malleable nsttutonal features, may affect the ablty of states to reach stable and effcent equlbra n ther customary nternatonal law relatons. * 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. George Norman and Joel Trachtman. All rghts reserved. The authors express apprecaton to those who made suggestons or commented on earler drafts, ncludng Jose Alvarez, Lucan Bebchuk, Davd Bederman, Marc Busch, Mchael Glennon, Ryan Goodman, Ian Johnstone, Lous Kaplow, Patrck Kelly, Davd Kennedy, Barbara Koremenos, Lsa Martn, Erc Posner, Mark Ramseyer, Kal Raustala, Alfred Rubn, Steven Shavell, Beth Smmons, Rchard Stenberg, Detlev Vagts and partcpants n semnars where ths paper was presented, at the Max Planck Insttute for Comparatve Publc Law and Internatonal Law, Harvard Law School, UCLA Law School and the Wharton School. We also thank Alexander Gazs and Chrstne Makor for research assstance. Errors are ours alone.

2 1 1. Introducton Customary nternatonal law (CIL) forms the nfrastructure of nternatonal law, and s also part of nternatonal law s superstructure. It thus serves as ts own foundaton, but also as the foundaton for treaty law, and therefore for essentally all nternatonal law. How frm s ths foundaton? CIL seems to have fallen on hard tmes, as t has been overtaken by treaty as the prncpal source of new rules n the nternatonal communty, as t often seems to be used by dealsts to make boot-strappng arguments about the content of nternatonal law, and as ts bndng force ts socal effect s often not readly apparent. 1 Ths at a tme when the domestc analog of CIL socal norms s the darlng of legal scholarshp. 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 trck of levtaton, s theoretcally plausble. 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. In addton, as a byproduct of the analyss supportng our central clam, we fnd that the CIL doctrne that has developed n order to dscrmnate between vald and nvald assertons of the exstence of rules of CIL s nternally coherent, and consstent wth our model s ratonalst perspectve on state behavor. Ths artcle refnes and extends an emergng ratonalst understandng of CIL. 2 Poneerng work n ths feld, notably that of Jack Goldsmth and Erc Posner, has begun 1 See generally, J. Patrck Kelly, The Twlght of Customary Internatonal Law, 40 VA. J. INT'L L. 449 (2000). 2 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 , avalable at 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 (1999) [herenafter Goldsmth & Posner 1999]; Andrew T. Guzman, A Complance-Based Theory of Internatonal Law, 90 CAL. L. REV (2002); Francesco Pars, The Formaton of Customary Law, George Mason Law and Economcs Research Paper No , Edward T. Swane, Ratonal

3 2 to artculate a ratonalst theory of CIL. Goldsmth and Posner have argued that CIL (a) does not exogenously affect state behavor and (b) s nternally ncoherent, as states are not motvated by opno jurs to comply wth CIL. 3 We show why the frst 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. The tautology 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 of behavor and therefore affect behavor through self-nterest. Whle CIL s endogenous to states as a group, t s an exogenous nfluence on the behavor of each ndvdual state. CIL may affect behavor even f t only does so at the margns. As to the second asserton, 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. Ths artcle develops an repeated mult-player prsoner s dlemma model of CIL. Of course, game theory can only provde a crude representaton of hghly nuanced decson-makng. 5 Our analyss focuses on parameters of the mult-player prsoner s dlemma n the CIL context: () 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, (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. 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 developng a postve theory suggestng the parameters for determnng whether CIL wll affect state behavor, ths artcle opens the way to normatve nsttutonal desgn. 6 States may determne to restructure certan 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). 3 The leadng artcle here s Goldsmth & Posner 1999, supra note 2. 4 By self-nterest we mean merely to refer to maxmzaton of preferences these preferences could be other-regardng or altrustc. 5 See the cautons expressed n Goldsmth & Posner 1999, supra note 2, and the broader treatment n Duncan Sndal, The Game Theory of Internatonal Poltcs, n Kenneth A. Oye, ed., COOPERATION UNDER ANARCHY (1986). 6 Danel A. Farber, Postve Theory as Normatve Crtque, 68 S. CAL. L. REV (1995).

4 3 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 attracts some scholars to socal norms 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 defnton of CIL and brefly locates ths artcle n relaton to four lteratures: law and economcs, socal norms, nternatonal organzaton and ndustral organzaton. Part 2 explans our choce of the repeated n-person prsoner s dlemma as the bass for our model, as well as our choce of an assumed strategy for players wthn ths model. Part 3 explans the other assumptons and parameters of our model. Part 4 sets forth the formal model. Part 5 presents some mplcatons n terms of () the plausblty of CIL, () polcy, () nternatonal law doctrne, and (v) research. Part 6 provdes some plausble examples of n-person CIL. Part 7 brefly concludes. a. Customary Internatonal Law and ts Doctrne As an ntroductory matter, t s useful to revew the fundamental defnton of CIL. 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. 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. 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 relates to the motvaton of states. Are states ever motvated by opno jurs? The ratonalst assumpton of states 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. 7 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 selfnterest. We respond to ths argument n part 5. 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 7 Goldsmth & Posner 1999, supra note 2.

5 4 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. 8 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. 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. The model set forth below 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 prohbts over-fshng n nternatonal waters? 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 game 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 they can be categorzed nto four game 8 Maurce H. Mendelson, The Formaton of Customary Internatonal Law, 272 RECUEIL DES COURS 155, (1998).

6 5 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 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 useful to emphasze 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. 9 Ther vews wth respect to coordnaton games are smlar. 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 fnd 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 10 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. 11 We may draw a rough, and lmted, analogy between the development of socal norms n a muncpal, or prvate settng, 12 and the development of CIL n the nternatonal Goldsmth & Posner 1999, supra note 2, at 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. 12 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

7 6 publc settng. In the nternatonal communty, CIL s substantvely smlar to the phenomenon Ellckson descrbes. 13 In nternatonal poltcal scence, regme theorsts such as Robert Keohane, 14 Stephen Krasner, and Beth Smmons 15 have told a smlar story of the possble rse of order n nternatonal socety. However, regme theory has generally avoded CIL. 16 Moreover, recognton that a rule has become part of CIL may sgnal ts support by, or lnkage wth, the mult- sector CIL 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). 17 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. 18 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 Revew: Sgnalng Dscount Rates: Law, Norms and Economc Methodology, 110 YALE L.J. 625 (2001). 13 For an example of ths type of analogcal allegory, comparng domestc custom to nternatonal custom, see Mendelson, supra note 8, at 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). 14 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). 15 See, e.g., STEPHEN D. KRASNER, INTERNATIONAL REGIMES (1983); Stephen D. Krasner & Beth Smmons, Theores of Internatonal Regmes, 41 INT L ORG. 491 (1987). 16 Duncan Sndal, Poltcal Economy and Internatonal Insttutons, 16 INT'L REV. L. & ECON. 121, 124 (1996). 17 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. 18 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.

8 7 enforce by means of socal sanctons. 19 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 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. 20 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. 21 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. Whle ths approach may have tracton n the CIL settng, and may re-emphasze the role of legtmacy, justce and moralty as bases for preference-modfcaton, ths artcle wll bypass that dscusson, and focus on exogenous explanatons of socal norms. 23 Modelng always nvolves 19 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. 20 See Harold Hongju Koh, Why Do Natons Obey Internatonal Law?, 106 YALE L.J (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). 21 See Robert D. Cooter, Expressve Law and Economcs, 27 J. LEG. STUDS. 585 (1998). 22 JON ELSTER, THE CEMENT OF SOCIETY 15 (1989). 23 Robert D. Cooter, Do Good Laws Make Good Ctzens? An Economc Analyss of Internalzed Norms, 86 VA. L. REV (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, (1998); JON ELSTER, THE CEMENT OF SOCIETY: A STUDY OF SOCIAL ORDER (1989). Basu refers to these as preference-changng norms.

9 8 smplfcaton, and our goal n ths paper s to elaborate a ratonalst model for future testng. In fact, testng a ratonalst model would help to clarfy the debate between exogenous preferences and endogenous preferences. In connecton wth exogenous explanatons, the law-based socal norms lterature has not embraced the repeated n-person prsoner s dlemma. 24 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 about ndvdual ratonalty: the subgame perfecton of thrd-party enforcement. 25 We address these concerns below.. Industral Organzaton Much of our understandng of the utlty, structure and dynamcs of n-person 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. An mportant concern for ndustral organzaton economsts s to dentfy crcumstances under whch such agreements can be made self-sustanng 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 paper, 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 problem. We wll dscuss some of these dstnctons based on payoff structures below. v. Internatonal Organzaton See Kaushk Basu, Socal Norms and the Law, 3 THE NEW PALGRAVE DICTIONARY OF ECONOMICS AND THE LAW 476 (1998). 24 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 n-person prsoner s dlemma. They explan that the objecton to these models s that thrd party enforcement s not ndvdually ratonal: that the ncentves of the players break down. 25 Id. at note 12, ctng work by Ellckson, Katz, McAdams and Posner.

10 9 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. 26 Ths lterature has not examned CIL. 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. 27 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. 28 The model we present here formalzes certan consderatons that reman nformal n much of the poltcal scence lterature, and has other varyng features that we descrbe below. 2. The N-Person Prsoner s Dlemma In ths secton we explan our choce of the n-person 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 n-person repeated prsoner s dlemma s really a group of varyng models, wth a number of varyng features, ncludng the number of players and ther preferences. 26 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 (1991); Duncan Sndal, Relatve Gans and the Pattern of Internatonal Cooperaton, 85 AM. POL. SCI. REV. 701 (1991). 27 See the specal ssue of Internatonal Organzaton devoted to the phenomenon of legalzaton. 54:3 INT L ORG. (2000). 28 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 (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, 577 (1992); Joel P. Trachtman, The Doman of WTO Dspute Resoluton, 40 HARV. INT'L L.J. 333, (1999).

11 10 a. Choce of Game As we consder the applcaton of game theory to the CIL settng, t should be noted that there s a wde choce of potental game structures to apply. 29 The basc payoff structure assumed n the prsoner s dlemma game captures the essental problem of cooperaton n a horzontal socal settng wth externaltes, 30 n whch partes have a choce between complance and defecton under crcumstances n whch they can enrch themselves ndvdually through defecton whle they could enrch socety through complance. 31 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. 32 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 n-person prsoner s dlemma can take account of a number of the dverse consderatons often referred to together as 29 For a useful analyss of the ft of other games, ncludng battle of the sexes and stag hunt, see Swane, supra note 2. 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). 30 By use of the term externaltes, we mean to be qute nclusve, ncludng both pecunary and non-pecunary externaltes: any crcumstance n whch an acton by one state has adverse or benefcal effects on another state. 31 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, whlemakng 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. 32 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).

12 11 reputaton or reputatonal sanctons. 33 We also beleve that the n-person prsoner s dlemma must be at the core of a ratonalst explanaton of the effectveness of socal norms. Fnally, we beleve that the n-person prsoner s dlemma offers parsmony: the factors that t takes nto account seem necessary, and there are no factors that seem superfluous. In a non-cooperatve, sngle-play crcumstance, wth a standard prsoner s dlemma payoff structure, we would expect non-complance. 34 Ths s each player s domnant strategy, and a Nash equlbrum 35 because under the payoffs assumed n the prsoner s dlemma, each party s better off defectng, no matter what the other party does. 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 unque Nash equlbrum s for both states to defect. 36 The same s true of a prsoner s dlemma game repeated a fnte number of tmes known n advance to the players. Now the unque sub-game perfect equlbrum s for each player to defect n each perod. A subgame perfect equlbrum s a strategy profle that nduces a Nash equlbrum n every subgame. 37 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 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 See Guzman, supra note 2. STEPHEN MARTIN, ADVANCED INDUSTRIAL ECONOMICS 98 (1993). A domnant strategy s one whch, no matter what the other player does, wll provde a hgher payoff to the actng player. 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). 36 Id. at M.J. OSBORNE, AN INTRODUCTION TO GAME THEORY (Oxford Unversty Press, 2004).

13 12 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. Our model s meant to show that there are substtutes for formal bndng agreements. In the CIL game, there are fve 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, the players can enter nto treates that are at least somewhat bndng. Thrd, 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. Fourth, 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. Ffth, 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 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. 38 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. 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. 39 Ostrom ctes consderable evdence regardng the amount and crcumstances of cooperaton by ndvduals n n-person 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 38 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). 39 Elnor Ostrom, Collectve Acton and the Evoluton of Socal Norms, 14:3 J. ECON. PERSP. 137, 138 (2000).

14 13 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 potentally stable and effcent equlbra n the n-person prsoner s dlemma, and suggest some possble approaches to emprcal testng. b. Choce of Strategy Wthn the prsoner s dlemma, we must postulate a partcular strategy for states to play. There are many choces. We menton only three: tt-for-tat, grm trgger, and penance.. Blateral or Multlateral Retalaton An mportant aspect of the structure of the game pertans to the ablty to mpose sanctons n a dscrmnatory manner. States may have trouble dscrmnatng n the applcaton of sanctons for several reasons. Frst, they may not be able to obtan nformaton regardng the author of the volaton. Ths mght occur, for example, wth respect to polluton at sea, or terrorst attack. Second, t may be costly for states to respond n a dscrmnatng way. For example, f the sancton nvolves trade barrers, the sanctonng state must nstruct ts customs offcers to dscrmnate among goods by orgn. Thrd, and most mportant, the relevant good beng produced by cooperaton may be non-excludable. Ths would occur wth the provson of publc goods or the protecton of nternatonal commons. To the extent that states are unable to dscrmnate, ther retalaton, f any, must be multlateral, nstead of blateral. Ths obvously lmts the strateges that they are able to play and the relatonshps that they may enter nto. Thus, gven that the strateges avalable to a state are cooperate or defect, there are at least two possbltes that we need to consder n connecton wth a multlateral game: () Defecton by state aganst state j leads to punshment of only by state j: blateral defecton leads to blateral punshment; or () Defecton by state aganst state j leads to punshment of by all states: blateral defecton leads to multlateral punshment. We focus our analyss on () for three reasons. Frst, t makes the analyss smpler wthout changng any of the qualtatve conclusons. Second, multlateral retalaton smply ncreases the ncentves to comply over blateral retalaton. Snce () nvolves mlder punshment of defecton than (), the condtons that support cooperaton wth blateral punshment under () wll certanly support cooperaton wth multlateral punshment under (). In other words, where multlateral punshment s possble, the condtons that we dentfy below are suffcent but not necessary to support a multlateral rule: any dscount factor that supports a multlateral CIL rule wth blateral punshment wll also support such a rule wth multlateral punshment. Thrd, there s some force to the argument that () s a more plausble scenaro than () n most of the stuatons n

15 14 whch the formulaton of CIL s lkely to be consdered. Artcles 42, 48 and 54 of the Internatonal Law Commsson s Rules on State Responsblty 40 generally prevent retalaton by thrd states for truly blateral njury, whle there seems no bass for retalaton by an njured state aganst non-njurng states. These rules seem to lmt the formal possblty for multlateral sanctons aganst truly blateral defecton. Thus, n our model, we assume that retalaton s appled blaterally that f state defects vs-à-vs state j, only state j wll respond, and only aganst state. If multple states responded aganst state, t would smply make cooperaton more lkely by ncreasng the punshment for defecton. Gven (), we can represent a multlateral prsoner s dlemma game as a set of blateral games, wth a typcal blateral game beng as specfed n Table 1 (page 29). As wll be seen below, ths s not the same as assumng a blateral game. Rather, t s a multlateral game wth blateral punshment.. 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, 41 t s not subgame perfect: after a defecton, the wronged state wll have ncentves to accept an undertakng from the defectng state that t wll cooperate n future. 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. Even more devastatng to tt-for-tat s the fact that once one state defects the game cycles endlessly between defecton and complance. 42. Grm Trgger Second, states may respond to defecton wth defecton forever: a blateral 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 40 Artcles on Responsblty of States for Internatonally Wrongful Acts, n Report of the Internatonal Law Commsson on the Work of Its Ffty-thrd Sesson, UN GAOR, 56th Sess., Supp. No. 10, at 43, UN Doc. A/56/10 (2001), avalable at < subsequently noted by the General Assembly n A/RES/56/83, Responsblty of States for Internatonally Wrongful Acts, adopted 12 Dec These artcles do not themselves represent nternatonal law, but are an attempt to codfy exstng custom. 41 See ROBERT AXELROD, THE EVOLUTION OF COOPERATION (1984). 42 Id., at 138.

16 15 to the one-shot Nash equlbrum of the prsoner s dlemma game. 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 subgame perfect, as t calls for a reverson to the domnant strategy of defecton n response to an ntal defecton. Goldsmth and Posner appear to recognze the possblty for stable and effcent equlbra under certan crcumstances where states play the grm trgger strategy. 43 However, usng an overfshng of commons context as ther example, they suggest that the grm trgger s not used and would be collectvely rratonal. In hs nterestng work on treates relatng to envronmental commons problems, 44 Barrett also rejects the grm trgger strategy because t fals to satsfy the crteron of collectve ratonalty. The collectve ratonalty consderaton s a formal artculaton of an 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 s subgame perfect as the reverson to the Nash equlbrum t s collectvely rratonal nsofar as ratonal negotators wll have ncentves to renegotate a cooperatve arrangement after defecton. Wth respect to the more emprcal queston of whether a grm trgger s 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 multlateral 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 theoretcal problem wth grm trgger s that because t s collectvely rratonal t s not renegotaton-proof. 45 That s, after a defecton, a coalton of states wll have ncentves to come together and cooperate wth the defector, deprvng the grm trgger of credblty and therefore effectveness. The reasonng s that equlbrum strateges that enforce cooperatve outcomes by the use of ths type of punshment can be undermned by the devator offerng to renegotate, proposng that the punshment phase be abandoned n favor of a return to cooperaton: a let bygones be bygones argument Goldsmth & Posner 1999, supra note 2, at 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). 45 See, e.g., Joseph Farrell & Erc Maskn, Renegotaton n Repeated Games, 1 GAMES & ECON. BEHAVIOR (1989); Fudenberg & Trole, supra note 36, at Indeed, ths s not uncommon n nternatonal law dscourse. See, e.g., Scott M. Sullvan, Changng The Premse Of Internatonal Legal Remedes: The Unfounded

17 16 An obvous counterargument to ths, of course, s that renegotaton unravels by forward nducton. 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? Also, 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. 47 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, an alternatve renegotaton-proof equlbrum s needed. We offer the penance strategy descrbed below as a weakly renegotaton proof alternatve. v. Penance Whle a precse defnton of renegotaton-proofness has not yet been agreed, the treatment by Farrell and Maskn s worth consderng. 48 They defne a weak renegotaton proof (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 s not WRP, snce after defecton the payoffs to cooperaton Pareto-domnate those of punshment. If renegotaton s possble and credble, the states wll prefer to renegotate after a defecton. Penance 49, by contrast, s subgame perfect and s weakly renegotatonproof. 50 Under penance, the response to defecton s counter-defecton that s contnued untl the orgnal defector accepts a perod of punshment after whch all players return to cooperaton. That s, n the event of defecton, the vctm retalates by defectng untl the ntal defector accepts a perod of punshment, by cooperatng whle the vctm defects. A form of penance seems to be endorsed by the Internatonal Law Commsson of the Unted Natons for applcaton n nternatonal law generally. Artcles 49 to 54 of the Artcles on State Responsblty provde that countermeasures may be used only to nduce Adopton Of Assurances And Guarantees Of Non-Repetton, 7 U.C.L.A. J. INT L L. & FOR. AFF. 265 ( ). 47 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 44, at Farrell & Maskn, supra note See Fudenberg & Trole, supra note 36, at Penance s sometmes referred to as gettng even. See ROGER B. MYERSON, GAME THEORY: ANALYSIS OF CONFLICT (1991). 50 Fudenberg & Trole, supra note 36, at 180, ctng Farrell & Maskn, supra note 45, at 327; Erc van Damme, Renegotaton-Proof Equlbra n Repeated Prsoner s Dlemma, 47 J. ECON. THEORY 206 (1989).

18 17 a state to cease a wrongful act and to make reparatons; 51 they must be commensurate wth the njury. 52 v. Equlbrum Selecton and Coordnaton One of the problems n an n-person prsoner s dlemma s dentfyng the strategy that other players are playng and coordnatng on a sngle strategy. Fudenberg and Trole conclude: Thus, repeated play wth patent players not only makes cooperaton meanng effcent payoffs possble, t also leads to a large set of other equlbrum outcomes. Several methods have been proposed to reduce ths multplcty of equlbra; however, none of them has yet been wdely accepted, and the problem remans a topc of research. 53 Under crcumstances of multple equlbra, anythng that tends to focus the players attenton on one partcular equlbrum, n a way that s commonly recognzed, tends to make ths the equlbrum that the players wll expect and thus actually mplement. 54 Whle there s no formal soluton to ths problem, states may coordnate through dplomacy, through other communcaton, or through ther actons advancng partcular customary rules. The selecton among multple equlbra may be understood as a separate, coordnaton game. Here, CIL, for example as reflected n the Rules of State Responsblty, may also play a role. 3. Assumptons Wthn the N-Person Prsoner s Dlemma Havng selected the n-person repeated prsoner s dlemma game, and the penance or grm trgger strategy, n ths secton, we develop the more specfc parameters and assumptons of our model. a. Effcency and Symmetry We assume that falure to reach a cooperatve equlbrum falure to reach an mplct agreement s neffcent. Of course, there are many crcumstances n whch no mplct agreement s needed, and reachng one would be neffcent. However, our goal s to examne strategc barrers to mplct agreement; reducng these barrers would always ncrease effcency, just as reducng the general barrers to contract between prvate partes would always ncrease effcency wthout requrng that partes contract n every crcumstance. Ths perspectve s consstent wth the frst theorem of welfare economcs, the Coase Theorem, and the effcency prncple : If people are able to bargan together effectvely, and can effectvely mplement and enforce ther decsons, then the outcomes of economc actvty wll tend to be effcent (at least for the partes to 51 See The Chorzow Factory Case, 1928 P.C.I.J., Ser. A, Nos. 7, 9, 17, 19 (oblgaton to make reparatons). 52 See Davd J. Bederman, Counterntutng Countermeasures, 96 AM. J. INT L L. 817 (2002). 53 Id. at Myerson, supra note 49, at 371.