Explaining Cooperation Under Anarchy: Hypotheses and Strategies Author(S): Kenneth A

Explaining Cooperation under Anarchy: Hypotheses and Strategies Author(s): Kenneth A. Oye Source: World Politics, Vol. 38, No. 1 (Oct., 1985), pp. 1-24 Published by: Cambridge University Press Stable URL: http://www.jstor.org/stable/2010349 . Accessed: 20/09/2011 21:10

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http://www.jstor.org EXPLAINING COOPERATION UNDER ANARCHY: Hypothesesand Strategies

By KENNETH A. OYE*

I. INTRODUCTION

N ATIONS dwell in perpetualanarchy, for no centralauthority imposes limitson the pursuitof sovereigninterests. This common condition gives rise to diverse outcomes. Relations among states are marked by war and concert,arms races and arms control,trade wars and tarifftruces, financial panics and rescues,competitive devaluation and monetarystabilization. At times, the absence of centralized international authorityprecludes attainmentof common goals. Because as states,they cannot cede ultimatecontrol over theirconduct to an supra- national sovereign, they cannot guarantee that they will adhere to their promises. The possibilityof a breach of promise can impede co- operationeven when cooperationwould leave all betteroff. Yet, at other times, states do realize common goals through cooperation under anarchy.Despite the absence of any ultimateinternational authority, gov- ernmentsoften bind themselves to mutually advantageous courses of action. And, though no internationalsovereign stands ready to enforce the terms of agreement,states can realize common intereststhrough tacit cooperation,formal bilateral and multilateralnegotiation, and the creation of internationalregimes. The question is: If internationalrelations can approximateboth a Hobbesian stateof natureand a Lockean civil society,why does cooperation emerge in some cases and not in others?' The contributorsto this symposium address both explanatoryand prescriptiveaspects of this perennial question. First,what circumstances favor the emergenceof cooperationunder anarchy? Given the lack of a

* I am gratefulfor commentsby JeffFrieden, Ralph Ginsberg,Joanne Gowa, Stephen Krasner,David Lake, Timothy McKeown, Paul Quirk, ArthurStein, and the other contributorsto this volume. The essays presentedhere focus on nation-statesas primaryactors in world politics, treat national preferencesas sovereign,and assume that any ultimateescape from internationalanarchy is unlikely.Our focusis on non-altruisticcooperation among statesdwelling in internationalanarchy. 2 WORLD POLITICS centralauthority to guaranteeadherence to agreements,what features of situationsencourage or permitstates to bind themselvesto mutually beneficialcourses of action?What featuresof situationspreclude cooperation?Second, what strategies can statesadopt to foster the emergence of cooperationby altering the circumstances they confront? Governments need not necessarilyaccept circumstances as given.To whatextent are situationalimpediments to cooperationsubject to willfulmodification? Throughwhat higher order strategies can statescreate the preconditions forcooperation? The problemof explainingand promotinginternational cooperation encompassesmany of the principal questions in thedisciplines of political economyand securitystudies. However, divergent terminological con- ventionsand substantiveapplications have impededthe comparisonof answers.In the essayspresented here, a unifiedanalytic framework, derivedfrom elementary game theoryand microeconomics,has been superimposedon cases in internationalsecurity and economicaffairs. This use of theaustere abstractions of game theoryand microeconomics offersseveral advantages.2First, superficial differences often obscure the parallelismof questions,explanations, and prescriptionsin the two fields. By reducing concepts to fundamentals,the use of elements of game theory and microeconomics permits ready identificationof parallels. Second, intrinsicdifferences between the politicsof war and the politics of wealth and welfare may give rise to divergent explanations and prescriptions.A unified analytic frameworkfacilitates explicit recognition of differencesin the extent and causes of, and prospects for, cooperation in securityand economic affairs.Finally, uneven intellectual developmentmay give rise to divergentexplanations and prescriptions. A unified analytic framework fosterstransference of useful concepts between the fields.3 In this introductoryessay, I submit that three circumstantialdimensions serve both as proximateexplanations of cooperationand as targets

2 In this essay, I use elementarygame theoryin a purely instrumentalfashion. First, although some referencesto the formalliterature are provided,the text does not furnish formalproofs on the existenceor location of equilibrium points in differentcategories of games. As Thomas Schelling notes, the equilibrium solutions identifiedby formal game theoristsmay stabilizeconvergent expectations among mathematicians,but unless equilibria can also be reached through"alternative less sophisticatedroutes," such solutionsmay have littleinfluence on internationaloutcomes. See Schelling,The Strategyof Conflict(London: Oxford UniversityPress, i963), II3-I4. Accordingly,the contributorssearch for "alternative less sophisticatedroutes" to reach mutuallybeneficial equilibrium points and for simple strategiesto restructuresituations to create mutuallybeneficial equilibrium points. 3 For an extendeddiscussion of the uses and abuses of game theoryin the empiricalstudy of internationalpolitics, see Duncan Snidal, "The Game Theoryof InternationalPolitics," in this collection. EXPLAINING COOPERATION UNDER ANARCHY 3 of longer-termstrategies to promotecooperation. Each of the threemajor sectionsof this piece definesa dimension,explains how that dimension accounts for the incidence of cooperationand conflictin the absence of centralized authority,and examines associated strategiesfor enhancing the prospectsfor cooperation. In the section entitled "Payoff Structure: Mutual and Conflicting Preferences,"I discuss how payoffsaffect the prospectsfor cooperation and present strategiesto improve the prospectsfor cooperation by al- teringpayoffs. Orthodox game theoristsidentify optimal strategiesgiven ordinally defined classes of games, and their familiar insightsprovide the startingpoint for the discussion.4Recent works in securitystudies, institutionalmicroeconomics, and internationalpolitical economy suggest strategiesto alter payoff structures and therebyimprove the prospects for cooperation.5 In the next section,entitled "Shadow of the Future: Single-playand Iterated Games," I discuss how the prospectof continuinginteraction affectsthe likelihood of cooperation;6examine how strategiesof reciprocitycan provide directpaths to cooperativeoutcomes under iterated conditions;7and suggeststrategies to lengthenthe shadow of the future.8 In addition,this section shows thatrecognition and controlcapabilities- the ability to distinguishbetween cooperation and defectionby others

4For the definitiveclassification of ordinallydefined games, see Anatol Rapoport and Melvin Guyer, "A Taxonomy of 2 X 2 Games," GeneralSystems ii (i966), 203-I4. For an extended reinterpretationof crisis bargaining in light of payoffstructures, see Glenn H. Snyder and Paul Diesing, ConflictAmong Nations: Bargaining,Decisionmaking, and System Structurein InternationalCrises (Princeton: Princeton University Press, I977). 5 For examples, see Robert Jervis,"Cooperation under the SecurityDilemma," World Politics30 (JanuaryI978), i67-214; Oliver E. Williamson, "Credible Commitments:Using Hostages to SupportExchange," American Economic Review (September i983), 5I9-40; John Gerard Ruggie, "InternationalRegimes, Transactions, and Change: Embedded Liberalism in the Postwar Economic Order," in Stephen D. Krasner,ed., InternationalRegimes (Ithaca, N.Y.: Cornell University,Press, i983). 6For orthodox game-theoreticanalyses of the importanceof iteration,see R. Duncan Luce and Howard Raiffa,Games and Decisions(New York: Wiley, I957), Appendix 8, and David M. Kreps, Paul Milgram,John Roberts, and RobertWilson, "Rational Cooperation in Finitely-RepeatedPrisoner's Dilemma," Journalof Economic Theory27 (August i982, 245-52. For the resultsof laboratoryexperiments, see Robert Radlow, "An Experimental Study of Cooperation in the Prisoner's Dilemma Game," Journalof ConflictResolution 9 (Junei965), 22I-27. On the importanceof indefiniteiteration to theemergence of cooperation in business transactions,see Robert Telsor, "A Theory of Self-EnforcingAgreements," Journalof Business53 (Januaryi980), 27-44. 7On how iteratedPrisoners' Dilemmas environmentsliterally select for Tit-for-Tat strategies, see Robert Axelrod, The Evolutionof Cooperation(New York: Basic Books, i984). For a formal statementon the effectsof reciprocityon equilibrium outcomes in iterated games, see Drew Fudenberg and Eric Maskin, "The Folk Theorem in Repeated Games with Discounting and with IncompleteInformation," Econometrica, forthcoming. 8 On enhancing iterativenessthrough decomposition of payoffsover time, see Schelling (fn. 2), 43-46, and Axelrod (fn. 7), I26-32. 4 WORLD POLITICS and to respondin kind-can affectthe power of reciprocity, and suggests strategiesto improve recognitioncapabilities.9 In the thirdsection, "Number of Players: Two-Person and N-Person Games," I explain why cooperationbecomes more difficultas the number of actors increases; present strategiesfor promotingcooperation in N- actor situations; and offerstrategies for promotingcooperation by reducing the number of actors necessary to the realization of common interests.Game theoristsand oligopoly theoristshave long noted that cooperation becomes more difficultas numbers increase, and their insightsprovide a startingpoint for discussions Recent work in political economy focuseson two strategiesfor promotingcooperation in thorny N-person situations:functionalist analysts of regimes suggest strategies for increasing the likelihood and robustnessof cooperationgiven large numbers of actors;" analystsof ad hoc bargaining in internationalpo- liticaleconomy suggest strategies of bilateraland regionaldecomposition to reducethe numberof actorsnecessary to the realizationof some mutual interests,at the expense of the magnitude of gains from cooperation.12 Each of the three circumstantialdimensions serves both as an explanationof cooperationand as a targetof strategiesto promotecooperation. The concluding section of this essay provides a roadmap to our efforts to test these preliminaryexplanations and strategies.By applying this common analytic frameworkto cases in economic and securityaffairs and by searching for explicit parallels and differencesin the incidence, causes, and prospectsfor cooperation,the authors hope to contributeto a deeper understandingof internationalcooperation.

II. PAYOFF STRUCTURE: MUTUAL AND CONFLICTING PREFERENCES

The structureof payoffsin a given round of play-the benefitsof mutual cooperation (CC) relative to mutual defection (DD) and the benefitsof unilateral defection(DC) relativeto unrequited cooperation (CD)-is fundamental to the analysis of cooperation. The argument

9Ibid., I39-4I- 10See Martin Shubik, Gamesfor Society,Business and War: TowardsA Theoryof Gaming (New York: Elsevier, I975). For a formalstatement on the importanceof the number of playersto cooperationin iteratedgames, see Fudenberg and Maskin (fn. 7). 11See Robert 0. Keohane, AfterHegemony: Cooperation and Discordin the WorldPolitical Economy(Princeton: Princeton University Press, i984), and Krasner (fn. 5). 12 See John A. C. Conybeare,"International Organization and the Theory of Property Rights,"International Organization 34 (Summer i980), 307-34, and Kenneth A. Oye, "Belief Systems,Bargaining, and Breakdown: InternationalPolitical Economy I929-I936," Ph.D. diss. (Harvard University,i983), chap. 3. EXPLAINING COOPERATION UNDER ANARCHY 5 proceedsin threestages. First, how does payoffstructure affect the significanceof cooperation? More narrowly, when is cooperation,defined in termsof consciouspolicy coordination, necessary to the realization of mutualinterests? Second, how does payoffstructure affect the likelihood and robustnessof cooperation?Third, through what strategies can statesincrease the long-termprospects for cooperation by altering payoffstructures? Beforeturning to thesequestions, consider briefly some tangible and intangibledeterminants of payoffstructures. The securityand political economyliteratures examine the effects of militaryforce structure and doctrine,economic ideology,the size of currencyreserves, macro- economiccircumstance, and a hostof otherfactors on nationalassess- mentsof nationalinterests. In "Cooperationunder the SecurityDi- lemma," RobertJervis has explainedhow the diffusionof offensive militarytechnology and strategiescan increaserewards from defection and therebyreduce the prospects for cooperation. In "InternationalRe- gimes,Transactions, and Chance:Embedded Liberalism in thePostwar EconomicOrder," John Ruggie has demonstratedhow thediffusion of liberaleconomic ideas increasedthe perceivedbenefits of mutualeco- nomic opennessover mutual closure(CC-DD), and diminishedthe perceivedrewards from asymmetric defection relative to asymmetric cooperation(DC-CD). In "Firmsand TariffRegime Change," Timothy McKeownhas shownhow downturnsin thebusiness cycle alter national tastesfor protection and therebydecrease the perceived benefits of mutual opennessrelative to mutual closureand increasethe perceived rewardsof asymmetricdefection.'3 In thepresent symposium, ideological and cognitivedeterminants of nationalpreferences are emphasizedin StephenVan Evera's essayon the originsof the First World War and KennethOye's chapteron monetaryconflict during the 1930s. RobertJervis's essay on the emergenceof concertfollowing systemic wars elucidates international struc- turaldeterminants of payoffs.John Conybeare's comparative study of tradewars, Kenneth Oye's studyof monetaryconflict in the 1930S, and CharlesLipson's studyof bankers'dilemmas examine macroeconomic determinantsof payoffstructure. George Downs, David Rocke, and RandolphSiverson investigate domestic structural determinants of payoffstructure in theiressay on cooperationin armsraces. Payoff structure

3 See Jervis(fn. 5); Ruggie (fn. 5); Timothy J. McKeown, "Firms and Tariff Regime Change: Explaining the Demand for Protection,"World Politics 36 (January1984), 215-33. On the effectsof ambiguity of preferenceson the prospectsof cooperation,see the concluding sectionsof Jervis(fn. 5). 6 WORLD POLITICS serves as an interveningvariable between cognitive,domestic, and internationalstructural factors and internationalcooperation.

A. PAYOFF STRUCTURE AND COOPERATION How does payoffstructure determine the significanceof cooperation? More narrowly,when is cooperation,defined in termsof conscious policy coordination,necessary to the realizationof mutualbenefits? For a mutual benefitto exist, actors must prefermutual cooperation (CC) to mutual defection(DD). For coordinationto be necessaryto the realization of the mutual benefit,actors must preferunilateral defection(DC) to unrequited cooperation(CD). These preferenceorderings are consistentwith the familiar games of Prisoners' Dilemma, Stag Hunt, and Chicken. Indeed, these games have attracteda disproportionateshare of scholarly attentionprecisely because cooperation is desirable but not automatic. In these cases, the capacityof statesto cooperate under anarchy,to bind themselvesto mutuallybeneficial courses of action withoutresort to any ultimatecentral authority, is vital to the realization of a common good. Many internationalsituations do not fall within this class of games. First, consider cases in which cooperation will not be necessaryto the realization of mutual interests.If actors preferunrequited cooperation (CD) to unilateral defection (DC), no incentive to cheat exists. The pursuit of self-interest,without regard to the action of others, will automaticallylead to mutual gains. For example, pure economic liberals-more common on economics facultiesthan in trade ministries- believe that unrequited openness is preferableto unilateral protection. Irrespectiveof the actions of others,a liberal believes that openness is best. In a world of pure liberals,policy coordination will not be necessary to the realization of openness. In such situations,where interestsare in full harmony,the capacity of states to cooperate under anarchy is ir- relevantto the realization of mutual benefits.'4 Second, consider cases where no mutual benefit can be realized through cooperation. If at least one actor prefersnominal mutual defection(DD) to nominal mutual cooperation(CC), "policycoordination" cannotlead to mutual gain; the term"cooperation" becomes inapplicable. Symmetricand asymmetricgames of Deadlock fall into this category. For example, if both the Soviet Union and the United States preferarms racingto arms control,conflict is inevitable.Or considera trade example: a believer in autarkywill prefermutual protectionto mutual openness. To speak of cooperationbetween a pure liberaland a believerin autarky

I4For an extended discussion of the distinctionbetween cooperationand harmony,see Keohane (fn. II), 5I-55. EXPLAINING COOPERATION UNDER ANARCHY 7 is nonsense. Where harmonyprevails, cooperation is unnecessaryto the realization of mutual interests.Where deadlocks exist, the term "cooperation" is devoid of meaning, and conflictis inevitable. Neither harmony nor deadlock has attractedsubstantial attention from game theorists-preciselybecause cooperativeand conflictualoutcomes follow so directlyand simply from the payoffstructure. What functiondo games of Harmony and Deadlock serve in this collection? In courses on diagnosis,medical studentsare taught,"When you hear hoofbeats,think horse beforeyou thinkzebra." Harrison Wag- ner has offeredsimilar advice to analystsof internationalrelations.15 He warned that Stag Hunt, Chicken, and Prisoners' Dilemma are often inappropriatemodels of internationalsituations. When you observecon- flict,think Deadlock-the absence of mutual interest-before puzzling over why a mutual interestwas not realized. When you observe cooperation,think Harmony-the absence of gains fromdefection-before puzzling over how states were able to transcend the temptationsof defection.By devotingsubstantial attention to the specificationof payoff structures,the contributorsseek to heed these warnings. In the class of games-including Prisoners'Dilemma, Stag Hunt, and Chicken-where cooperation is necessaryto the realization of mutual benefits,how does payoffstructure affect the likelihood and robustness of cooperation in these situations? Cooperation will be less likely in Prisoners'Dilemma than in Stag Hunt or Chicken. To understandwhy, consider each of these games in conjunctionwith the illustrativestories fromwhich they derive their names. Prisoners'Dilemma: Two prisonersare suspected of a major crime. The authoritiespossess evidence to secure convictionon only a minor charge. If neitherprisoner squeals, both will draw a light sentence on the minor charge (CC). If one prisonersqueals and the otherstonewalls, the rat will go free(DC) and the sucker will draw a veryheavy sentence (CD). If both squeal, both will draw a moderate sentence (DD). Each prisoner'spreference ordering is: DC > CC > DD > CD. If theprisoners expect to "play" only one time,each prisonerwill be betteroff squealing than stonewalling,no matterwhat his partnerchooses to do (DC > CC and DD > CD). The temptationof the rat payoffand fearof the sucker payoffwill drive single-play Prisoners' Dilemmas toward mutual defection.Unfortunately, if both prisonersact on this reasoning,they will draw a moderate sentenceon the major charge,while cooperationcould have led to a light sentenceon the minor charge (CC > DD). In single-

I5Wagner, "The Theory of Games and the Problem of InternationalCooperation," AmericanPolitical Science Review 70 (June i983), 330-46. 8 WORLD POLITICS play Prisoners' Dilemmas, individuallyrational actions produce a col- lectivelysuboptimal outcome. Stag Hunt: A group of hunters surround a stag. If all cooperate to trap the stag, all will eat well (CC). If one person defects to chase a passing rabbit,the stag will escape. The defectorwill eat lightly(DC) and none of the others will eat at all (CD). If all chase rabbits,all will have some chance of catching a rabbit and eating lightly(DD). Each hunter'spreference ordering is: CC > DC > DD > CD. The mutual interestin plentifulvenison (CC) relativeto all otheroutcomes militates stronglyagainst defection.However, because a rabbitin the hand (DC) is betterthan a stag in the bush (CD), cooperationwill be assured only if each hunter believes that all hunters will cooperate. In single-play Stag Hunt, the temptationto defectto protectagainst the defectionof othersis balanced by the stronguniversal preference for stag over rabbit.'6 Chicken: Two drivers race down the centerof a road from opposite directions. If one swerves and the other does not, then the firstwill sufferthe stigma of being known as a chicken (CD) while the second will enjoy being known as a hero (DC). If neither swerves,both will suffergrievously in the ensuing collision (DD). If both swerve,damage to the reputationof each will be limited (CC). Each driver'spreference orderingis: DC > CC > CD > DD. If each believes thatthe otherwill swerve, then each will be tempted to defect by continuingdown the centerof the road. Betterto be a live hero than a live chicken. If both succumb to this temptation,however, defectionwill result in collision. The fear that the other driver may not swerve decreases the appeal of continuing down the center of the road. In single-playChicken, the temptationsof unilateral defectionare balanced by fear of mutual defection.17 In games that are not repeated, only ordinally defined preferences matter.Under single-playconditions, interval-level payoffs in ordinally defined categories of games cannot (in theory)affect the likelihood of cooperation.In the illustrationsabove, discussionsof dominantstrategies

i6 KennethWaltz borrowedRousseau's parableof thestaghunt to illustratethe infeasibility of realizing mutual interestsunder internationalanarchy. Rousseau used the staghuntto illustratethe possibilityof cooperationduring his firstperiod of primativesocial interde- pendence. He argued that individualscould cooperateon "mutual undertakings"to realize "presentand perceptibleinterest" through "some kind of freeassociation that obligated no one and lasted only so long as the passing need that formed it." This essay returnsto Rousseau's use of the staghunt.See Waltz, Man, the State,and War (New York: Columbia UniversityPress, 1959), and JeanJacques Rousseau: The Firstand Second Discourses,trans. Roger D. and JudithR. Masters(New York: St. Martins,i964), 165-67. I The illustrativepreference orderings strike most mature observersas perverse: the driversneed not place themselvesin the game. EXPLAINING COOPERATION UNDER ANARCHY 9 do not hingeon the magnitudeof differencesamong the payoffs.Yet the magnitudeof differencesbetween CC and DD and betweenDC and CD can be large or small,if not preciselymeasurable, and can increaseor decrease.Changes in the magnitudeof differencesin the value placed on outcomescan influencethe prospectsfor cooperation throughtwo paths. First,changes in the value attachedto outcomescan transformsit- uations fromone ordinallydefined class of game into another.For example,in "Cooperationunder the SecurityDilemma" RobertJervis describedhow difficultPrisoners' Dilemmas may evolve into less chal- lengingStag Hunts if thegains from mutual cooperation (CC) increase relativeto thegains from exploitation (DC). He relatedthe structure of payoffsto traditionalconcepts of offensiveand defensivedominance, and offensiveand defensivedominance to technologicaland doctrinal shifts.Ernst Haas, MaryPat Williams,and Don Babai haveemphasized theimportance of cognitive congruence as a determinantof technological cooperation.The diffusionof commonconceptions of the natureand effectsof technologyenhanced perceived gains fromcooperation and diminishedperceived gains fromdefection, and mayhave transformed some Prisoners'Dilemmas into Harmony.'8 Second, under iteratedconditions, the magnitudeof differences among payoffswithin a givenclass of games can be an importantde- terminantof cooperation.The moresubstantial the gains frommutual cooperation(CC-DD) and theless substantialthe gains from unilateral defection(DC-CD), thegreater the likelihood of cooperation. In iterated situations,the magnitudeof the differencebetween CC and DD and betweenDC and CD in presentand futurerounds of playaffects the likelihoodof cooperation in thepresent. This pointis developedat length in the sectionon the shadowof thefuture.

B. STRATEGIES TO ALTER PAYOFF STRUCTURE If payoffstructure affects the likelihood of cooperation, to whatextent can statesalter situations by modifyingpayoff structures, and thereby increasethe long-term likelihood of cooperation?Many of thetangible and intangibledeterminants of payoffstructure, discussed at theoutset of this section,are subjectto willfulmodification through unilateral, bilateral,and multilateralstrategies. In "Cooperationunder the Security Dilemma," RobertJervis has offeredspecific suggestions for altering payoffstructures through unilateral strategies. Procurement policy can

i8 Haas, Williams, and Babai, Scientistsand WorldOrder: The Usesof TechnicalKnowledge in InternationalOrganizations (Berkeley: University of CaliforniaPress, I977). 10 WORLD POLITICS affectthe prospectsfor cooperation. If one superpowerfavors procure- mentof defensiveover offensiveweapons, it can reduceits own gains fromexploitation through surprise attack (DC) and reduceits adversary's fearof exploitation(CD). Membersof allianceshave oftenresorted to the device of deployingtroops on troubledfrontiers to increasethe likelihoodof cooperation.A state'suse of troopsas hostagesis designed to diminishthe payoff from its own defection-toreduce its gains from exploitation(DC)-and therebyrender defensive defection by its partner less likely.Publicizing an agreementdiminishes payoffs associated with defectionfrom the agreement,and therebylessens gains fromexploitation.These observationsin internationalrelations are paralleledby recentdevelopments in microeconomics.Oliver Williamsonhas iden- tifiedunilateral and bilateraltechniques used byfirms to facilitateinter- firmcooperation by diminishinggains fromexploitation. He distin- guishesbetween specific and nonspecificcosts associated with adherence to agreements.Specific costs, such as specializedtraining, machine tools, and construction,cannot be recoveredin the eventof the breakdown ofan agreement.When parties to an agreementincur high specific costs, repudiationof commitments will entail substantial losses. Firms can thus reducetheir gains from exploitation through the technique of acquiring dedicatedassets that serve as hostagesto continuingcooperation. Non- specificassets, such as general-purposetrucks and airplanes,are sal- vageableif agreements break down; firms can reducetheir fear of being exploitedby maximizingthe use of nonspecificassets, but such assets cannotdiminish gains fromexploitation by servingas hostages.'9Uni- lateral strategiescan improve the prospectsof cooperation by reducing both the costs of being exploited (CD) and the gains from exploitation (DC). The new literatureon interfirmcooperation indirectlyraises an old question on the costs of unilateralstrategies to promotecooperation in internationalrelations. In many instances,unilateral actions that limit one's gains from exploitation may have the effectof increasingone's vulnerabilityto ex- ploitationby others.For example,a statecould limitgains fromdefection fromliberal internationaleconomic norms by permittingthe expansion of sectors of comparative advantage and by permittingliquidation of inefficientsectors. Because a specialized economy is a hostage to international economic cooperation,this strategywould unquestionablyin- crease the credibilityof the nation's commitmentto liberalism. It also

I9Williamson (fn. 5). EXPLAINING COOPERATION UNDER ANARCHY 11 has the effect,however, of increasingthe nation's vulnerability to pro- tectionby others. In thetroops-as-hostage example, the government that stationstroops may promotecooperation by diminishingan ally'sfear of abandonment,but in so doingit raisesits own fearsof exploitation by theally. In an examplefrom the neoconservative nuclear literature, Paul Nitze, Colin Gray,William Van Cleave,and othersassume that missileswill be firedagainst missiles rather than against industries or cities,and concludethat a shiftfrom counterforce toward countervalue weapons may purchasea reductionin gains fromexploitation at the expenseof heightenedvulnerability to exploitation.2oCognitive, domestic,and internationalstructural factors affect payoff structure directly, and also influenceperceptions of the benefitsand limitsof unilateral strategiesto alterpayoffs. Unilateralstrategies do not exhaustthe rangeof optionsthat states mayuse to alterpayoff structures. Bilateral strategies-most significantly strategiesof issue linkage-can be used to alter payoffstructures by combiningdissimilar games. Because resortto issue linkagegenerally assumesiteration, analysis of how issue linkagecan be used to alter payoffsis presentedin the sectionon the shadow of the future.Fur- thermore,bilateral "instructional" strategies can aim at alteringanother country'sunderstanding of cause-and-effectrelationships, and resultin alteredperceptions of interest.For example,American negotiators in SALT I soughtto instructtheir Soviet counterpartson the logic of mutual assured destruction.21 Multilateral strategies,centering on the formationof international regimes,can be used to alter payoffstructures in two ways. First,norms generated by regimes may be internalized by states,and therebyalter payoffstructure. Second, informationgenerated by regimes may alter states' understanding of their interests.As Ernst Haas argues, new regimes may gather and distribute informationthat can highlight cause-and-effectrelationships not previously understood. Changing perceptionsof means-ends hierarchiescan, in turn, result in changing perceptions of interest.22

20 See Paul Nitze, "Assuring StrategicStability in an Era of Detente," ForeignAffairs 54 (JanuaryI976), 207-32, for the seminal article in this tradition.Nitze's recommendations hinge on acceptance of the preceptsof what has come to be known as nuclear utilization theory.Jervis's recommendations depend on acceptance of the preceptsof mutual assured destruction(fn. 5).

21 See JohnNewhouse, Cold Dawn: The Storyof SALT I (New York: Holt, Rinehart& Winston, I973). 22 See Haas, "Words Can Hurt You; Or Who Said What to Whom About Regimes," in Krasner (fn. 5). 12 WORLD POLITICS

III. THE SHADOW OF THE FUTURE: SINGLE-PLAY AND ITERATED GAMES The distinctionbetween cases in whichsimilar transactions among partiesare unlikelyto be repeatedand cases in whichthe expectation offuture interaction can influencedecisions in thepresent is fundamental to theemergence of cooperationamong egotists. As theprevious section suggests,states confronting strategic situations that resemble single-play Prisoners'Dilemma and, to a lesserextent, single-play Stag Hunt and Chicken,are constantlytempted by immediategains fromunilateral defection,and fearfulof immediatelosses from unrequited cooperation. How does continuinginteraction affect prospects for cooperation? The argumentproceeds in four stages.First, why do iteratedconditions improvethe prospectsfor cooperation in Prisoners'Dilemma and Stag Hunt whilediminishing the prospects for cooperation in Chicken?Sec- ond, how do strategiesof reciprocityimprove the prospectsfor cooperationunder iterated conditions? Third, why does theeffectiveness of reciprocityhinge on conditionsof play-the abilityof actorsto distinguishreliably between cooperation and defectionby othersand to respondin kind? Fourth,through what strategiescan statesimprove conditionsof playand lengthenthe shadowof the future?23 Beforeturning to thesequestions, consider the attributesof iterated situations.First, states must expect to continuedealing with each other. This conditionis, in practice,not particularly restrictive. With the possible exceptionof global thermonuclearwar, internationalpolitics is characterizedby the expectatonof futureinteraction. Second, payoff structuresmust not change substantially over time. In otherwords, each roundof play shouldnot alterthe structure of thegame in the future. This conditionis, in practice,quite restrictive.For example,states con- sideringsurprise attack when offense is dominantare in a situationthat has manyof the characteristics ofa single-playgame: attack alters options and payoffsin futurerounds of interaction.Conversely, nations consid- eringincreases or decreasesin theirmilitary budgets are in a situation thathas manyof the characteristics ofan iteratedgame: spending options and associatedmarginal increases or decreasesin militarystrength are likelyto remainfairly stable over futurerounds of interaction.In internationalmonetary affairs, governments considering or fearingde- valuationunder a gold-exchangestandard are in a situationthat has manyof the characteristicsof a single-playgame: devaluationmay diminishthe value of anotherstate's foreign currency reserves on a one-

23 This section is derived largelyfrom Axelrod (fn. 7), and Telsor (fn. 6). EXPLAINING COOPERATION UNDER ANARCHY 13 time basis, while reductionsin holdingsof reserveswould diminish possiblelosses on a one-timebasis. Conversely, governments considering interventionunder a floatingsystem with minimalreserves are in a situationthat has manyof the characteristicsof an iteratedgame: de- preciationor appreciationof a currencywould not producesubstantial one-timelosses or gains.Third, the size of thediscount rate applied to thefuture affects the iterativeness of games. If a governmentplaces little value on futurepayoffs, its situationhas manyof thecharacteristics of a single-playgame. If itplaces a highvalue on futurepayoffs, its situation mayhave manyof thecharacteristics of an iteratedgame. For example, politicalleaders in theirfinal term are likelyto discountthe future more substantiallythan political leaders running for, or certainof, reelection.

A. THE SHADOW OF THE FUTURE AND COOPERATION How does the shadowof the futureaffect the likelihood of cooperation?Under single-playconditions without a sovereign,adherence to agreementsis oftenirrational. Consider the single-playPrisoners' Di- lemma.Each prisoneris betteroff squealing, whether or nothis partner decides to squeal. In the absenceof continuinginteraction, defection would emergeas thedominant strategy. Because the prisoners can nei- therturn to a centralauthority for enforcementof an agreementto cooperatenor relyon the anticipationof retaliationto deterpresent defection,cooperation will be unlikelyunder single-play conditions. If theprisoners expect to be placed in similarsituations in thefuture, the prospectsfor cooperation improve. Experimental evidence suggests that under iteratedPrisoners' Dilemma the incidenceof cooperationrises substantially.24Even in theabsence of centralizedauthority, tacit agree- mentsto cooperatethrough mutual stonewalling are frequentlyreached and maintained.Under iterated Prisoners' Dilemma, a potentialdefector comparesthe immediate gain fromsquealing with the possible sacrifice of futuregains thatmay resultfrom squealing.25 In single-playStag

24 See Anatol Rapoportand AlbertChammah, Prisoner's Dilemma (Ann Arbor: University of Michigan Press, i965), and subsequentessays in Journalof ConflictResolution. 25 One commonobjection to thisline of argumentcenters on theirrationality of cooperation if a sequence of Prisoners'Dilemmas has a known last element.On the known last play, the immediategain fromsquealing cannot be offsetby expectationsof futurecooperation. On the next-to-lastplay, the immediategain fromsquealing is not offsetby expectations of futurecooperation, since both actorsknow thatcooperation is irrationalon the last move. And so on back toward the initialmove. This line of analysiscollapses iteratedPrisoners' Dilemma into single-playPrisoners' Dilemma. To analystsof internationalrelations, the importanceof this objection is limited.In internationalrelations, no experimenterdecrees that a series of Prisoners'Dilemmas shall end on the ioth move or at noon. Althoughany series of transactionswill terminatesooner or later,governments do not generallyknow when the last play will occur. On all rounds of play, the actors' decisions are conditioned 14 WORLD POLITICS Hunt, each hunteris temptedto defectin orderto defendhimself against the possibilityof defection by others. A reputation for reliability,for resistingtemptation, reduces the likelihood of defection.If the hunters are a permanentgroup, and expectto hunt togetheragain, the immediate gains fromunilateral defectionrelative to unrequited cooperationmust be balanced against the cost of diminished cooperationin the future.In both Prisoners' Dilemma and Stag Hunt, defection in the present decreasesthe likelihood of cooperation in the future.In both, therefore, iterationimproves the prospectsfor cooperation.26In Chicken, iteration may decrease the prospectsfor cooperation. Under single-playconditions, the temptation of unilateral defection is balanced by the fear of the collision that follows frommutual defection.How does iterationaffect this balance? If the game is repeated indefinitely,then each driver may refrain from swerving in the present to coerce the other driver into swerving in the future.Each driver may seek to acquire a reputation fornot swervingto cause the otherdriver to swerve.In iteratedChicken, one driver's defectionin the presentmay decrease the likelihood of the other driver's defectionin the future.27

B. STRATEGIES OF RECIPROCITY AND CONDITIONS OF PLAY It is at this juncture that strategyenters the explanation. Although the expectation of continuing interactionhas varying effectson the likelihood of cooperation in the illustrationsabove, an iteratedenviron- ment permits resort to strategiesof reciprocitythat may improve the prospectsof cooperation in Chicken as well as in Prisoners' Dilemma and Stag Hunt. Robert Axelrod argues thatstrategies of reciprocityhave the effectof promotingcooperation by establishinga direct connection between an actor's presentbehavior and anticipatedfuture benefits. Tit- for-Tat,or conditional cooperation,can increase the likelihood of joint cooperation by shaping the futureconsequences of presentcooperation or defection.

by the possibilityof futureinteraction. For a formalanalysis of how uncertaintime horizons can lead to a resolutionof the Prisoners'Dilemma, see Luce and Raiffa(fn. 6), Appendix 8. Discount parameterssuch as Axelrod's"w" maycapture the effects of uncertainty.Possible futurepayoffs may be discountedboth because the value placed on futurebenefits is lower than presentbenefits and because the streamof futurebenefits may be interruptedif the structureof the game changes. 26 This conclusion restson the assumptionthat dyadic interactionsare moderatelyin- dependent.For an argumenton how defectioncan provide a benefit(external to a dyadic interaction)by discouragingthe entryof other actors,see Shibley Telhami, "Cooperation or Coercion: Tit for Tat and the Realities of InternationalPolitics," unpub. (Swarthmore College, Januaryi985). Note also that cooperationcan also encourage (mutuallybeneficial) entryof other actors. 27 On iteratedChicken, see Snyderand Diesing (fn. 4), 43-44. EXPLAINING COOPERATION UNDER ANARCHY 15 In iterated Prisoners' Dilemma and Stag Hunt, reciprocityunder- scoresthe futureconsequences of presentcooperation and defection.The argument presented above-that iterationenhances the prospects for cooperation in these games-rests on the assumption that defectionin the present will decrease the likelihood of cooperation in the future. Adoption of an implicit or explicit strategyof matching stonewalling with stonewalling,squealing with squealing, rabbitchasing with rabbit chasing,and cooperativehunting with cooperativehunting validates the assumption. In iteratedChicken, a strategyof reciprocitycan offsetthe perverse effectsof reputationalconsiderations on the prospectsfor cooperation.Recall that in iteratedChicken, each drivermay refrainfrom swerving in the present to coerce the other driver into swerving in the future. Adoption of an implicit or explicit strategyof Tit-for-Tat in iteratedgames of Chicken alters the futurestream of benefitsassociated with present defection.If a strategyof reciprocityis credible, then the mutual losses associated with future collisions can encourage present swerving.In all threegames, a promiseto respondto presentcooperation with future cooperation and a threat to respond to present defection with futuredefection can improve the prospectsfor cooperation. The effectivenessof strategiesof reciprocityhinges on conditionsof play-the ability of actors to distinguishreliably between cooperation and defection by others and to respond in kind. In the illustrations provided above, the meaning of "defect" and "cooperate" is unambig- uous. Dichotomous choices-between squeal and stonewall, chase the rabbitor capture the stag, continuedown the road or swerve-limit the likelihood of misperception.Further, the actions of all are transparent. Given the definitionsof the situations,prisoners, hunters, and drivers can reliably detect defectionand cooperation by other actors. Finally, the definitionof the actorseliminates the possibilityof controlproblems. Unitary prisoners,hunters, and drivers do not sufferfrom factional, organizational, or bureaucratic dysfunctionsthat might hinder imple- mentationof strategiesof reciprocity. In internationalrelations, conditions of play can limitthe effectiveness of reciprocity.The definitionof cooperationand defectionmay be ambiguous. For example, the Soviet Union and the United States hold to markedlydifferent definitions of "defection"from the termsof detente as presented in the Basic Principles Agreement;28the European Com- munity and the United States differover whether domestic sectoral policies comprise indirectexport subsidies. Further,actions may not be

28 See Alexander L. George, Managing U.S.-SovietRivalry: Problems of CrisisPrevention (Boulder, CO: Westview, i983). 16 WORLD POLITICS transparent.For example,governments may not be able to detectone another'sviolations of armscontrol agreements or indirectexport subsidies. If defectioncannot be reliablydetected, the effectof present cooperationon possiblefuture reprisals will erode. Together, ambiguous definitionsand a lack of transparencycan limitthe abilityof statesto recognizecooperation and defectionby others. Becausereciprocity requires flexibility, control is as importantas recognition.Internal factional, organizational, and bureaucraticdysfunc- tionsmay limit the ability of nations to implementTit-for-Tat strategies. It maybe easierto sellone unvaryingline of policy than to sella strategy of shiftingbetween lines of policyin responseto the actionsof others. For example,arms suppliersand defenseplanners tend to resistthe cancellationof weaponssystems even if the cancellation is a responseto the actionsof a rival. Import-competingindustries tend to resistthe removalof barriersto imports,even if trade liberalization is in response to liberalizationby anotherstate. At times,national decision makers maybe unableto implementstrategies of reciprocity. On otheroccasions, theymust invest heavily in sellingreciprocity. For thesereasons, national decisonmakers may displaya bias againstconditional strategies: the domesticcosts of pursuingsuch strategies may partially offset the value of the discountedstream of futurebenefits that conditional policies are expectedto yield. As RobertAxelrod notes, problems of recognitionand controlmay limiteffective resort to reciprocity.In thissymposium, such problems are examinedin severalways. The essay on "Arms Races and Co- operation"presents a simplesimulation designed to assessthe sensitivity of Tit-for-Tatstrategies to departuresfrom perfect recognition and control.The case studiesand the conclusionassess the extent to which problemsof recognitionand controlare, in practice,impediments to effectiveutilization of strategiesof reciprocity.29

C. STRATEGIES TO IMPROVE RECOGNITION AND LENGTHEN THE SHADOW OF THE FUTURE To what extentcan governmentspromote cooperation by creating favorableconditions of play and by lengtheningthe shadow of the future?The literatureon internationalregimes offers several techniques forcreating favorable conditions of play.Explicit codification of norms

29 Axelrod shows thatin iteratedPrisoners' Dilemma, whereactors can reliablydistinguish between cooperation and defectionby others and respond in kind, Tit-for-Tatperforms better than do alternativestrategies. When recognitionand control are perfect,iterated environmentsstrongly favor the emergenceof cooperation. EXPLAINING COOPERATION UNDER ANARCHY 17 can limitdefinitional ambiguity. The veryact of clarifyingstandards of conduct,of defining cooperative and uncooperativebehavior, can permit moreeffective resort to strategiesof reciprocity.Further, provisions for surveillance-forexample, mechanisms for verification in armscontrol agreementsor for sharinginformation on the natureand effectsof domesticsectoral policies-can increasetransparency. In practice,the goal ofenhancing recognition capabilities is oftencentral to negotiations underanarchy. The game-theoreticand institutionalmicroeconomic literatures offer severalapproaches to increasingthe iterativecharacter of situations. Thomas Schellingand RobertAxelrod suggest tactics of decomposition over time to lengthenthe shadow of the future.30For example,the temptationto defectin a deal promisingthirty billion dollars for a billion barrelsof oil may be reducedif the deal is sliced up into a seriesof paymentsand deliveries.Cooperation in armsreduction or in territorial disengagementmay be difficultif the reduction or disengagementmust be achievedin one jump.If a reductionor disengagementcan be sliced up intoincrements, the problem of cooperationmay be renderedmore tractable.Finally, strategies of issuelinkage can be used to alterpayoff structuresand to interjectelements of iterativenessinto single-play situations.Relations among states are rarelylimited to one single-playissue ofoverriding importance. When nationsconfront a single-playgame on one issue,present defection may be deterredby threats of retaliationon otheriterated issues. In internationalmonetary affairs, for instance, a governmentfearing one-time reserve losses if another state devalues its currencymay link devaluation to an iteratedtrade game. By establishing a directconnection between present behavior in a single-playgame and futurebenefits in an iteratedgame, tacit or explicitcross-issue linkage can lengthenthe shadowof the future.3' The shadowof thefuture, strategies of reciprocity,and payoffstruc- tureinteract in determiningthe likelihood of cooperation.Incentives to cooperateand to defectare thediscounted stream of anticipatedpayoffs acrosscurrent and futureencounters. The size ofthe discount rate affects the value of futurebenefits. A Tit-for-Tatstrategy provides a clearer view of how presentbehavior is likelyto affectan adversary'sfuture behavior,and therebysharpens differences between the anticipated

3- Schelling (fn. 2), 43-46, and Axelrod (fn. 7), i26-32. 3' For analyses of issue linkage, see Robert D. Tollison and Thomas D. Willett, "An Economic Theory of MutuallyAdvantageous Issue Linkages in InternationalNegotiations," InternationalOrganization 33 (Autumn I979) 425-49; Oye (fn. i2), chap. 3, "Bargaining:The Logic of Contingent Action"; and Axelrod and Keohane in the concluding essay of this symposium. 18 WORLD POLITICS streamof payoffsfor cooperation and defection.The structureof payoffs in each round of play is the object of the discountingand anticipating.

IV. NUMBER OF PLAYERS: Two-PERSON AND N-PERSON GAMES

Up to now, I have discussed the effectsof payoffstructure and the shadow of the futureon the prospectsof cooperation in terms of two- person situations.What happens to the prospectsfor cooperationas the number of significantactors rises? In this section, I explain why the prospectsfor cooperation diminish as the number of players increases; examine the functionof internationalregimes as a responseto the problems created by large numbers; and offer strategiesto improve the prospectsfor cooperationby alteringsituations to diminish the number of significantplayers. The numbers problem is centralto many areas of the social sciences. Mancur Olson's theoryof collectiveaction focuseson N-person versions of Prisoners' Dilemma. The optimism of our earlier discussions of cooperationunder iteratedPrisoners' Dilemma gives way to the pessimism of analyses of cooperation in the provisionof public goods. Applications of Olsonian theoryto problems ranging from cartelizationto the pro- vision of public goods in alliances underscorethe significanceof "free- riding" as an impediment to cooperation.32In internationalrelations, the numbersproblem has been centralto two debates. The longstanding controversyover the stabilityof bipolar versusmultipolar systems reduces to a debate over the impact of the number of significantactors on internationalconflict.33 A more recentcontroversy, between proponents of the theoryof hegemonic stabilityand advocates of internationalregimes, reduces to a debate over the effectsof large numbers on the robustnessof cooperation.34

32 See Mancur Olson, Jr.,The Logic of CollectiveAction: Public Goods and the Theoryof Groups (Cambridge: Harvard UniversityPress, i965), and Mancur Olson and Richard Zeckhauser, "An Economic Theory of Alliances," Review of Economicsand Statistics48 (August1966), 266-79. For a recentelegant summaryand extensionof the large literature on dilemmas of collective action, see Russell Hardin, CollectiveAction (Baltimore: Johns Hopkins UniversityPress, i982). 33See Kenneth N. Waltz, "The Stabilityof a Bipolar World," Daedalus 93 (Summer i964), and Richard N. Rosecrance,"Bipolarity, Multipolarity, and the Future,"Journal of ConflictResolution (September I966), 3 14-27. 34On hegemony,see Robert Gilpin, U.S. Power and the MultinationalCorporation (New York: Basic Books, I975), 258-59. On duopoly,see TimothyMcKeown, "Hegemonic Stability Theory and i9th-CenturyTariff Levels in Europe," InternationalOrganization 37 (Winter i983), 73-9I. On regimes and cooperation,see Keohane (fn. ii), and Krasner (fn. 5). On two-persongames and N-person public-goodsproblems, see Charles Kindleberger,"Dom- inance and Leadership in the InternationalEconomy: Exploitation,Public Goods, and Free Rides," InternationalStudies Quarterly 25 (June i98i), 242-54. EXPLAINING COOPERATION UNDER ANARCHY 19

A. NUMBER OF PLAYERS AND COOPERATION How do numbersaffect the likelihoodof cooperation?There are at leastthree important channels of influence.35First, cooperation requires recognitionof opportunitiesfor the advancement of mutualinterests, as wellas policycoordination once these opportunities have been identified. As the numberof playersincreases, transactions and informationcosts rise. In simpleterms, the complexityof N-personsituations militates againstidentification and realizationof commoninterests. Avoiding nuclearwar duringthe Cuban missilecrisis called forcooperation by theSoviet Union and theUnited States. The transactionand information costsin thisparticularly harrowing crisis, though substantial, did not precludecooperation. By contrast,the problem of identifyingsignificant actors,defining interests, and negotiatingagreements that embodied mutualinterests in theN-actor case of I9I4 was farmore difficult. These secondarycosts associated with attainingcooperative outcomes in N- actorcases erode the difference between CC and DD. Moresignificantly, theintrinsic difficulty of anticipatingthe behavior of otherplayers and of weighingthe value of thefuture goes up withthe number of players. The complexityof solving N-person games, even in thepurely deductive sense,has stuntedthe developmentof formalwork on the problem. This complexityis even greaterin real situations,and operatesagainst multilateralcooperation. Second,as the numberof playersincreases, the likelihoodof autonomous defectionand of recognitionand controlproblems increases. Cooperativebehavior rests on calculationsof expectedutility-merging discountrates, payoff structures, and anticipatedbehavior of other players.Discount rates and approachesto calculationare likelyto varyacross actors,and the prospectsfor mutualcooperation may declineas the numberof playersand the probableheterogeneity of actorsincreases. The chancesof includinga statethat discounts the futureheavily, that is too weak (domestically)to detect,react, or implementa strategyof reciprocity,that cannotdistinguish reliably between cooperation and defectionby otherstates, or thatdeparts from even minimalstandards ofrationality increase with the number of states in a game.For example, manypessimistic analyses of the consequencesof nuclearproliferation focuson how breakdownsof deterrencemay become more likely as the numberof countrieswith nuclear weapons increases.36 Third,as thenumber of players increases, the feasibility of sanctioning defectorsdiminishes. Strategies of reciprocitybecome more difficult to

35See Keohane (fn. ii), chap. 6, for extensionsof these points. 36 See Lewis A. Dunn, Controllingthe Bomb (New Haven: Yale UniversityPress, i982). 20 WORLD POLITICS implementwithout triggeringa collapse of cooperation. In two-person games, Tit-for-Tatworks well because the costsof defectionare focused on only one other party.If defectionimposes costs on all parties in an N-person game, however,the power of strategiesof reciprocityis undermined. The infeasibilityof sanctioningdefectors creates the possibility of free-riding.What happens if we increase the number of actors in the iterated Prisoners' Dilemma from 2 to 20? Confession by any one of them could lead to the convictionof all on the major charge; therefore, the threatto retaliateagainst defectionin the presentwith defectionin the futurewill impose costson all prisoners,and could lead to wholesale defectionin subsequent rounds. For example, under the I9I4 systemof alliances, retaliationagainst one member of the alliance was the equiv- alent of retaliationagainst all. In N-person games, a strategyof conditional defectioncan have the effectof spreading,rather than contain- ing, defection.

B. STRATEGIES OF INSTITUTIONALIZATION AND DECOMPOSITION Given a large number of players, what strategiescan states use to increase the likelihood of cooperation?Regime creationcan increase the likelihoodof cooperationin N-person games.37First, conventions provide rules of thumb that can diminish transactionand informationcosts. Second, collectiveenforcement mechanisms both decrease the likelihood of autonomous defectionand permit selectivepunishment of violators of norms. These two functionsof internationalregimes directly address problems created by large numbers of players.For example, Japan and the members of NATO professa mutual interestin limitingflows of militarilyuseful goods and technologyto the Soviet Union. Obviously, all suppliers of militarilyuseful goods and technologymust cooperate to deny the Soviet Union access to such items. Although governments differin theirassessment of the militaryvalue of some goods and tech- nologies, there is consensus on a ratherlengthy list of prohibiteditems. By facilitatingagreement on the prohibitedlist, the CoordinatingCom- mittee of the Consultative Group of NATO (CoCom) provides a rela- tively clear definitionof what exports would constitutedefection. By definingthe scope of defection,the CoCom list forestallsthe necessity of retaliationagainst nations that ship technologyor goods that do not fall within the consensual definitionof defection.38Generally, cooper-

37 In addition to providinga partial solutionto the problemsof large numbers,regimes may affectthe order and intensityof actor preferencesas normsare internalized,and may heightenthe iterativenessof situationsas interactionbecomes more frequent. 38 For a full analysis of intra-alliancecooperation on East-West trade, see Michael Mastanduno, "Strategiesof Economic Containment:U.S. Trade Relations with the Soviet EXPLAINING COOPERATION UNDER ANARCHY 21 ation is a prerequisiteof regimecreation. The creationof rules of thumb and mechanisms of collective enforcementand the maintenance and administrationof regimes can demand an extraordinarydegree of cooperation. This problem may limit the range of situationssusceptible to modificationthrough regimist strategies. What strategiescan reduce the number of significantplayers in a game and therebyrender cooperation more likely? When governments are unable to cooperateon a global scale,they often turn to discriminatory strategiesto encourage bilateral or regional cooperation.Tactics of decomposition across actors can, at times, improve the prospects for cooperation. Both the possibilitiesand the limits of strategiesto reduce the number of players are evident in the discussionsthat follow. First, reductionsin the number of actors can usually only be purchased at the expense of the magnitude of gains from cooperation. The benefitsof regional openness are smaller than the gains from global openness. A bilateralclearing arrangement is less economicallyefficient than a multilateral clearingarrangement. Strategies to reduce the numberof players in a game generally diminish the gains from cooperation while they increasethe likelihood and robustnessof cooperation.39Second, strategies to reduce the number of players generally impose substantialcosts on third parties. These externalitiesmay motivate third parties to undermine the limited area of cooperation or may serve as an impetus for a thirdparty to enlarge the zone of cooperation.In the I930s, forexample, wholesale resortto discriminatorytrading policies facilitatedcreation of exclusive zones of commercialopenness. When confrontedby a shrink- ing market share, Great Britain adopted a less liberal and more discriminatorycommercial policy in order to secure preferentialaccess to its empire and to undermine preferentialagreements between other countries.As the American market share diminished,the United States adopted a more liberal and more discriminatorycommercial policy to increaseits access to exportmarkets. It is not possible,however, to reduce the number of players in all situations.For example, compare the example of limited commercial openness with the example of a limited strategicembargo. To reduce the numberof actorsin a tradewar, market access can simply be offeredto only one countryand withheld from others.By contrast,defection by only one supplier can permitthe target

Union," WorldPolitics 37 (Julyi985), 503-3I, and BeverlyCrawford and StephanieLenway, "Decision Modes and InternationalRegime Change: WesternCollaboration on East-West Trade, WorldPolitics 37 (April i985), 375-402. 39 For a pure libertarianargument on privateexchange as an alternativeto public man- agement,see Conybeare (fn. i2). 22 WORLD POLITICS of a strategicembargo to obtain a criticaltechnology. These problems may limit the range of situationssusceptible to modificationthrough strategiesthat reduce the number of players in games.

IV. CONCLUSION As I noted at the outset, the analytic approach presented in this symposium constitutesan implicit attack on the traditionalboundary between studiesof internationalpolitical economy and studiesof security. The emphasis on cooperation,the reliance on the three circumstantial dimensions,and the analysisof associatedstrategies to altercircumstances are not specificto eithersecurity affairs or politicaleconomy. This essay and Duncan Snidal's complementaryintroduction, "The Game Theory of International Politics," define and operationalize the three sets of abstractexplanatory and prescriptivepropositions, and discuss the uses and abuses of game theoryin the empiricalstudy of internationalpolitics. The six empirical essays in the main body of this collection provide a limitedtrial of thesepropositions by probingdiverse situations, strategies, and outcomes in both securityand economic affairs.40 In the firstof the three case studies in securityaffairs, Robert Jervis explains the incidence,scope, and duration of great-powerconcerts. He begins by noting that counterhegemonicwar appears to be a necessary condition for the emergence of concert,and then offersan explanation of why the Concert of Europe lasted from i8I5 to i854, but attempts at concertfollowing World Wars I and II collapsed. His analysisstresses the effects of an international structural cause-counterhegemonic war-and of concert itselfon the preconditionsfor cooperation. Stephen Van Evera explains the collapse of a fragilepeace in I9I4. His analysis stresses the effectsof a family of ideas-militarism, na- tionalism,and social imperialism-on the governingelites' perceptions of theirinterests and of each other.Van Evera suggeststhat these ideas undermined each of the threesituational preconditions for cooperation, and are necessaryto the explanationof the outbreak of the First World War. George Downs, David Rocke, and Randolph Siversontranscend some of the superficialcontroversies over strategythat divide analystsof arms control.Their essay identifiesconditions that determine when unilateral

4 See Alexander George and Richard Smoke,Deterrence in AmericanForeign Policy (New York: Columbia UniversityPress, I974) fora seminalexample of how an austeretheoretical frameworkand detailed historicalcases can promote both development of theory and historicalunderstanding. EXPLAINING COOPERATION UNDER ANARCHY 23 action, tacit bargaining,and explicitnegotiation are likely to reduce the intensityof arms races. Their analysis of i9th- and 20th-centuryarms races thatdid not terminatein war stressesthe effectsof payoffstructure and of problems of recognitionand control on the efficacyof armscontrol strategies. In the firstof the case studies in political economy,John Conybeare examines factorsthat may promoteand inhibitcommercial cooperation. He explains why cooperation was not robust during the perpetual it- erationsof the Anglo-Hanse conflict,how asymmetriesof power initially impeded cooperation in the late i9th-centuryFranco-Italian case, and how the "publicness" of the Hawley-Smoot tariffimpeded cooperation during the I930s. Between I930 and I936, internationalmonetary relations were marked by the collapse of fixed exchange rates and resortto competitivedeval- uation, the emergenceof bilateraland regional cooperation,and limited monetarycoordination under the Tripartite Stabilization Agreement. Kenneth Oye considerscircumstantial and strategicdeterminants of the incidence and scope of monetarycooperation in the I930s. In timesof financialcrisis, individual creditorscan derive benefitfrom limitingtheir exposure to protectthemselves against default. But if many creditorslimit their exposure, default is assured. In his essay, Charles Lipson notes that contemporarydebt rescheduling requires the cooperation of literallyhundreds of creditors,and explains how private sanctionsand institutionalsettings have fosteredcooperation (to date). By juxtaposing a generic analytic frameworkand two sets of cases organized along traditionalsubdisciplinary boundaries, the contributors to thiscollection encourage speculationalong several lines. First,to what extentdo cases in securityaffairs and political economy tend to fall into differentareas of the space definedby the threesituational dimensions? Second, to what extent does readiness to resort to associated sets of strategiesappear to differin securityaffairs and political economy? Third, what aspects of cooperationin securityaffairs and political economy are not explained by the core approach employed in this volume? Finally,what additional situationaland strategicvariables might improve the quality of explanation? In the concludingessay, Robert Axelrod and RobertKeohane consider these questions. They begin by examining the fit between observed cooperation and conflict,and the three sets of situationalpreconditions. They then review the case studies,assessing the possibilitiesand limits of strategiesto alter payoffstructure, to lengthen the shadow of the futureand create favorableconditions of play, and to reduce numbers 24 WORLD POLITICS of players,with particular emphasis on reciprocityand regimebuilding. Axelrodand Keohane ultimatelymove towarda new synthesis.They suggestthat international regimes can reinforceand institutionalizerec- iprocity,and thatnations have enhancedthe prospectsfor cooperation by relyingon a combinationof atomisticreciprocity and regimeestab- lishment.