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Trustees of Princeton University 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 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Cambridge University Press and Trustees of Princeton University are collaborating with JSTOR to digitize, preserve and extend access to World Politics. http://www.jstor.org EXPLAINING

COOPERATION UNDER ANARCHY: and Strategies Hypotheses By KENNETH A. OYE* I. INTRODUCTION N ATIONS dwell in perpetualanarchy,forno 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,financialpanics and rescues,competitivedevaluation and monetarystabilization.At times,the absence of centralized international authorityprecludes attainmentof common goals. Because as states,theycannot cede ultimatecontrolover theirconduct to an supranational sovereign, they cannot guarantee that they will adhere to their promises. The possibilityof a breach of promise can impede cooperationeven when cooperationwould leave all betteroff.Yet, at other times,states do realize common goals throughcooperation under anarchy.Despite the absence of any ultimateinternationalauthority,governmentsoften bind themselvesto mutually

advantageous courses of action. And, though no internationalsovereignstands ready to enforce the terms of agreement,states can realize common intereststhrough tacit cooperation,formalbilateraland multilateralnegotiation,and the creation of internationalregimes. The question is: If internationalrelationscan approximateboth a Hobbesian stateof natureand a Lockean civil society,why does cooperation emerge in some cases and not in others? The contributorsto this symposiumaddress both explanatoryand prescriptiveaspects of this perennialquestion. First,what circumstances favor the emergenceof cooperationunderanarchy?Given the lack of a * I am gratefulfor commentsby JeffFrieden, Ralph Ginsberg,JoanneGowa, Stephen Krasner,David Lake, Timothy McKeown, Paul Quirk, ArthurStein, and the othercontributorsto this volume. The essays presentedhere focus on nation-statesas primaryactors in world politics, treat national preferencesas sovereign,and assume that any ultimateescape from

internationalanarchyis unlikely.Our focusis on non-altruistic cooperationamong statesdwelling in internationalanarchy. 2 WORLD POLITICS whatfeatures to guaranteeadherenceto agreements, centralauthority to mutually encourageor permitstatesto bindthemselves of situations beneficialcoursesof action?What featuresof situationsprecludecocan statesadopttofostertheemergence operation?Second,whatstrategies Governments theyconfront? byalteringthecircumstances of cooperation as given.To whatextentare acceptcircumstances need notnecessarily to cooperationsubjectto willfulmodification? situationalimpediments can statescreatethepreconditions Throughwhathigherorderstrategies forcooperation? international cooperation The problemof explainingand promoting ofpolitical manyoftheprincipalquestionsinthedisciplines encompasses conterminological economyand securitystudies.However,divergent of comparison the applicationshave impeded ventionsand substantive answers.In the essayspresentedhere,a

unifiedanalyticframework, has been game theoryand microeconomics, derivedfromelementary securityand economicaffairs. superimposedon cases in international and microeconomics ofgametheory This use oftheaustereabstractions offersseveral advantages.2First,superficialdifferencesoftenobscure 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, intrinsicdifferencesbetween the politicsof war and the politics of wealth and welfare may give rise to divergent explanations and prescriptions.A unified analyticframeworkfacilitatesexplicit recognition of differencesin the extent and causes of, and prospects for, cooperation in securityand economic affairs.Finally, uneven intellectual developmentmay give rise to divergentexplanationsand prescriptions. A unified analytic framework fosterstransferenceof useful concepts between the fields.3

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In this introductoryessay, I submit that threecircumstantialdimensions serve both as proximateexplanationsof cooperationand as targets 2 In this essay, I use elementarygame theoryin a purely instrumentalfashion.First, although some referencesto the formalliteratureare provided,the textdoes not furnish formalproofson the existenceor location of equilibriumpoints in differentcategoriesof games. As Thomas Schelling notes, the equilibrium solutions identifiedby formalgame but unless equilibria theoristsmay stabilizeconvergentexpectationsamong mathematicians, can also be reached through"alternativeless sophisticatedroutes,"such solutionsmay have littleinfluenceon internationaloutcomes.See Schelling,The Strategyof Conflict(London: searchfor"alternative Accordingly,the contributors OxfordUniversityPress, i963), II3-I4. less sophisticatedroutes" to reach mutuallybeneficialequilibrium points and for simple strategiesto restructuresituationsto

createmutuallybeneficialequilibriumpoints. 3 For an extendeddiscussionof 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 oflonger-termstrategiesto promotecooperation.Each of thethreemajor 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 payoffsaffectthe prospectsfor cooperation and present strategiesto improve the prospectsfor cooperation by alteringpayoffs.Orthodox game theoristsidentifyoptimal strategiesgiven ordinally defined classes of games, and their familiarinsightsprovide the startingpoint for the discussion.4Recent works

in securitystudies, institutionalmicroeconomics,and internationalpolitical economy suggeststrategiestoalterpayoffstructuresand therebyimprovetheprospects 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 suggeststrategiesto lengthenthe shadow of the future.8 In addition,thissectionshows thatrecognitionand controlcapabilitiesthe abilityto distinguishbetween cooperation and defectionby others 4For the definitiveclassificationof ordinallydefinedgames, see Anatol Rapoport and Melvin Guyer, "A Taxonomy of 2 X 2 Games," GeneralSystemsii (i966), 203-I4. For an extended reinterpretation of crisis bargainingin light of payoffstructures,see Glenn H. Snyder and Paul Diesing, ConflictAmongNations:Bargaining,Decisionmaking, and

System Structurein InternationalCrises(Princeton:PrincetonUniversityPress, 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,"AmericanEconomicReview(Septemberi983), 5I9-40; John Gerard Ruggie, "InternationalRegimes,Transactions,and Change: Embedded Liberalism in the Postwar Economic Order," in StephenD. Krasner,ed., International Regimes(Ithaca, N.Y.: Cornell University, Press, i983). 6For orthodox game-theoreticanalyses of the importanceof iteration,see R. Duncan Luce and Howard Raiffa,Gamesand Decisions(New York: Wiley, I957), Appendix 8, and David M. Kreps, Paul Milgram,JohnRoberts,and RobertWilson, "Rational Cooperation in Finitely-RepeatedPrisoners Dilemma," Journalof Economic Theory27 (August i982, 245-52. For the resultsof laboratoryexperiments,see Robert Radlow, "An Experimental Study

of Cooperation in the PrisonersDilemma Game," Journalof ConflictResolution9 (Junei965), 22I-27. On theimportanceof indefiniteiterationto theemergenceofcooperation in business transactions,see Robert Telsor, "A Theory of Self-EnforcingAgreements," Journalof Business53 (Januaryi980), 27-44. 7On how iteratedPrisonersDilemmas environments literallyselectforTit-for-Tatstrategies, 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 iterativeness throughdecompositionof payoffsover time, see Schelling (fn. 2), 43-46, and Axelrod (fn. 7), I26-32. 4 WORLD POLITICS and torespondin kind-can affect thepowerofreciprocity, and suggests strategiesto improve recognitioncapabilities.9 In the

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thirdsection,"Number of Players: Two-Person and N-Person Games," I explain whycooperationbecomesmore difficult as thenumber of actors increases; presentstrategiesfor promotingcooperation in Nactor situations; and offerstrategiesfor promotingcooperation by reducing the number of actors necessaryto the realization of common interests.Game theoristsand oligopoly theoristshave long noted that cooperation becomes more difficultas numbers increase,and their insightsprovide a startingpoint fordiscussions Recent work in political economy focuseson two strategiesforpromotingcooperationin thorny N-person situations:functionalistanalystsof regimessuggest strategies for increasingthe likelihood and robustnessof cooperationgiven large numbers of actors;" analystsof ad hoc bargaining in internationalpoliticaleconomysuggeststrategiesof bilateraland regionaldecomposition to reducethenumberofactorsnecessaryto therealizationof some mutual interests,at the expense of the magnitude of gains

from cooperation.12 Each of the threecircumstantialdimensionsservesboth as an explanationof cooperationand as a targetof strategiesto promotecooperation. The concluding sectionof 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 searchingfor explicitparallels and differencesin the incidence, causes, and prospectsforcooperation,the authors hope to contributeto a deeper understandingof internationalcooperation. II. PAYOFF MUTUAL STRUCTURE: AND CONFLICTING PREFERENCES The structureof payoffsin a given round of play-the benefitsof mutual cooperation (CC) relative to mutual defection (DD) and the benefitsof unilateraldefection(DC) relativeto unrequited cooperation fundamental to the analysis of cooperation. The argument (CD)-is 9Ibid., I39-4I10See Martin Shubik, Gamesfor Society,Businessand War: TowardsA Theoryof Gaming (New York: Elsevier, I975).

For a formalstatementon the importanceof the number of playersto cooperationin iteratedgames, see Fudenberg and Maskin (fn. 7). 11See Robert0. Keohane, AfterHegemony:Cooperationand Discordin the WorldPolitical Economy(Princeton:PrincetonUniversityPress, i984), and Krasner (fn. 5). See JohnA. C. Conybeare,"InternationalOrganization and the Theory of Property Rights,"International Organization34 (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. 12 EXPLAINING COOPERATION UNDER ANARCHY 5 affectthe proceedsin threestages.First,how does payoffstructure significance defined Morenarrowly, whenis cooperation, ofcooperation? necessaryto the realization in termsof consciouspolicycoordination, affectthelikeSecond,how does payoffstructure of mutualinterests? of cooperation?Third,throughwhat strategies lihoodand robustness prospectsforcooperationby

altering can statesincreasethe long-term payoffstructures? sometangibleand Beforeturningto thesequestions,considerbriefly determinants of and political The security payoffstructures. intangible of military forcestructure and examinetheeffects economyliteratures doctrine,economic ideology,the size of currencyreserves,macroand a hostof otherfactorson nationalassesseconomiccircumstance, mentsof nationalinterests.In "Cooperationunder the SecurityDilemma,"RobertJervishas explainedhow the diffusionof offensive and strategies can increaserewardsfromdefection military technology In "International Reand thereby forcooperation. reducetheprospects and Chance:EmbeddedLiberalismin thePostwar gimes,Transactions, EconomicOrder,"JohnRuggiehas demonstrated how thediffusion of of mutualecoliberaleconomicideas increasedthe perceivedbenefits nomic opennessover mutual closure(CC-DD), and diminishedthe defectionrelativeto asymmetric perceivedrewardsfromasymmetric In Tariff "Firms

and RegimeChange,"Timothy cooperation (DC-CD). in thebusinesscyclealternational McKeownhas shownhowdownturns of mutastesforprotection and thereby decreasetheperceivedbenefits tual opennessrelativeto mutual closureand increasethe perceived defection.3 rewardsof asymmetric of In thepresentsymposium, ideologicaland cognitivedeterminants nationalpreferences are emphasizedin StephenVan Everas essayon the originsof the First World War and KennethOyes chapteron conflictduringthe 1930s. RobertJerviss essayon theemermonetary strucwarselucidatesinternational genceof concertfollowingsystemic studyof turaldeterminants of payoffs. JohnConybearescomparative conflict in the 1930S, and tradewars,KennethOyes studyof monetary CharlesLipsonsstudyof bankersdilemmasexaminemacroeconomic determinants of payoffstructure. George Downs, David Rocke,and of paydomesticstructural determinants RandolphSiversoninvestigate offstructure in theiressayon cooperation in armsraces.Payoffstructure 3 See Jervis(fn. 5);

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Ruggie (fn. 5); Timothy J. McKeown, "Firms and Tariff Regime Change: Explaining the Demand forProtection,"WorldPolitics36 (January1984), 215-33. On the effectsofambiguityof preferences on the prospectsof cooperation,see the concluding sectionsof Jervis(fn. 5). 6 WORLD POLITICS serves as an interveningvariable between cognitive,domestic,and internationalstructuralfactorsand internationalcooperation. A. PAYOFF STRUCTURE AND COOPERATION How does payoffstructuredeterminethe significanceof cooperation? More narrowly,when is cooperation,definedin termsof conscious policy coordination,necessaryto the realizationof mutualbenefits? For a mutual benefitto exist,actors must prefermutual cooperation (CC) to mutual defection(DD). For coordinationto be necessaryto the realizationof the mutual benefit,actors must preferunilateral defection(DC) to unrequited cooperation(CD). These preferenceorderingsare consistentwith the familiar games of Prisoners Dilemma, Stag Hunt, and Chicken.

Indeed, these games have attracteda disproportionateshare of scholarly attentionpreciselybecause cooperation is desirable but not automatic. In these cases, the capacityof statesto cooperateunder anarchy,to bind themselvesto mutuallybeneficialcoursesof action withoutresortto any ultimatecentralauthority,is vital to the realizationof a common good. Many internationalsituationsdo 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 ministriesbelieve 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,policycoordinationwill 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 irrelevantto 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; theterm"cooperation"becomesinapplicable. Symmetricand asymmetricgames of Deadlock fall into this category. For example, if both the Soviet Union and theUnited Statespreferarms racingto arms control,conflictis inevitable.Or considera tradeexample: a believer in autarkywill prefermutual protectionto mutual openness. To speak of cooperationbetweena 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,cooperationis unnecessaryto the realization of mutual interests.Where deadlocks exist, the term "cooperation" is devoid of meaning, and conflictis inevitable. Neither harmony nor deadlock has attractedsubstantialattentionfrom game theorists-preciselybecause cooperativeand conflictualoutcomesfollow so directlyand simplyfromthe payoffstructure. What functiondo games of Harmony and Deadlock serve in this collection?In courses on diagnosis,medical studentsare taught,"When you hear hoofbeats,thinkhorsebeforeyou thinkzebra." Harrison Wagner has offeredsimilaradvice to analystsof internationalrelations.15 He warned that Stag Hunt, Chicken, and Prisoners Dilemma are often inappropriatemodels of internationalsituations.When you observeconflict,thinkDeadlock-the absence of mutual interest-before puzzling over why a mutual interestwas not realized. When you observe cooperation,thinkHarmony-the absence ofgains

fromdefection-before puzzling over how states were able to transcend the temptationsof defection.By devotingsubstantialattentionto the specificationof payoff structures,the contributorsseek to heed these warnings. In the class of games-including PrisonersDilemma, Stag Hunt, and Chicken-where cooperation is necessaryto the realization of mutual benefits,how does payoffstructureaffectthe likelihood and robustness of cooperation in these situations? Cooperation will be less likely in PrisonersDilemma than in Stag Hunt or Chicken. To understandwhy, consider each of these games in conjunctionwith the illustrativestories fromwhich theyderive theirnames. PrisonersDilemma: Two prisonersare suspected of a major crime. The authoritiespossess evidence to secure convictionon only a minor charge. If neitherprisonersqueals, 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 suckerwill draw a veryheavy sentence

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(CD). If both squeal, both will draw a moderate sentence (DD). Each prisonerspreferenceorderingis: DC > CC > DD > CD. If theprisoners expectto "play" onlyone time,each prisonerwill be betteroffsquealing than stonewalling,no matterwhat his partnerchooses to do (DC > CC and DD > CD). The temptationof the rat payoffand fearof the sucker payoffwill drive single-playPrisoners Dilemmas toward mutual defection.Unfortunately,if both prisonersact on this reasoning,theywill draw a moderate sentenceon the major charge,while cooperationcould have led to a lightsentenceon the minor charge (CC > DD). In singleI5Wagner, "The Theory of Games and the Problem of InternationalCooperation," AmericanPoliticalScience Review 70 (June i983), 330-46. 8 WORLD POLITICS play Prisoners Dilemmas, individuallyrational actions produce a collectivelysuboptimal outcome. Stag Hunt: A group of hunterssurround a stag. If all cooperate to trap the stag, all will eat well (CC). If

one person defectsto 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 hunterspreferenceorderingis: 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 bythestronguniversalpreferenceforstagover rabbit.6 Chicken:Two driversrace down the centerof a road fromopposite 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 neitherswerves,both will

suffergrievouslyin the ensuing collision (DD). If both swerve,damage to the reputationof each will be limited (CC). Each driverspreference orderingis: DC > CC > CD > DD. If each believesthatthe 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 resultin 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-levelpayoffsin ordinally defined categoriesof games cannot (in theory)affectthe likelihood of cooperation.In the illustrationsabove, discussionsof dominantstrategies i6 KennethWaltz borrowedRousseaus parableof thestaghuntto illustratetheinfeasibility of

realizing mutual interestsunder internationalanarchy.Rousseau used the staghuntto illustratethe possibilityof cooperationduring his firstperiod of primativesocial interdependence. He argued that individualscould cooperateon "mutual undertakings"to realize "presentand perceptibleinterest"through"some kind of freeassociationthatobligatedno one and lasted only so long as the passing need that formedit." This essay returnsto Rousseaus use of the staghunt.See Waltz, Man, theState,and War (New York: Columbia UniversityPress, 1959), and JeanJacquesRousseau: The Firstand SecondDiscourses,trans. Roger D. and JudithR. Masters(New York: St. Martins,i964), 165-67. I The illustrativepreferenceorderingsstrike most mature observersas perverse:the driversneed not place themselvesin the game. EXPLAINING COOPERATION UNDER ANARCHY 9 Yet amongthe payoffs. do not hingeon the magnitudeof differences betweenCC and DD and betweenDC the magnitudeof differences and CD can be

large or small,if not preciselymeasurable,and can in the increaseor decrease.Changes in the magnitudeof differences value placed on outcomescan influencethe prospectsforcooperation throughtwo paths. sitFirst,changesin the value attachedto outcomescan transform uationsfromone ordinallydefinedclass of game into another.For example,in "Cooperationunderthe SecurityDilemma" RobertJervis PrisonersDilemmasmayevolveintoless chaldescribedhow difficult (CC) increase lengingStag Huntsifthegainsfrommutualcooperation of (DC). He relatedthestructure relativeto thegainsfromexploitation dominance, defensive and of offensive payoffsto traditionalconcepts and doctrinal and defensivedominanceto technological and offensive shifts. ErnstHaas, MaryPat Williams,and Don Babai haveemphasized oftechnological as a determinant congruence ofcognitive theimportance of the natureand of common conceptions The diffusion cooperation. enhancedperceivedgains fromcooperationand effectsof technology and mayhave

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transformed diminishedperceivedgainsfromdefection, somePrisonersDilemmasintoHarmony.8 Second, under iteratedconditions,the magnitudeof differences dewithina givenclass of gamescan be an important amongpayoffs thegainsfrommutual The moresubstantial of cooperation. terminant thegainsfromunilateral cooperation(CC-DD) and theless substantial In iterated defection (DC-CD), thegreaterthelikelihoodofcooperation. DD and and CC between the difference of the magnitude situations, betweenDC and CD in presentand futureroundsof playaffectsthe This pointis developedat length in thepresent. likelihoodofcooperation in thesectionon theshadowof thefuture. B. STRATEGIES TO ALTER PAYOFF STRUCTURE towhatextent thelikelihoodofcooperation, affects If payoff structure and thereby payoffstructures, can statesaltersituationsby modifying Manyof thetangible likelihoodof cooperation? increasethelong-term discussedat theoutset of payoffstructure, determinants and intangible throughunilateral, of thissection,are

subjectto willfulmodification In "CooperationundertheSecurity and multilateral strategies. bilateral, Dilemma," RobertJervishas offeredspecificsuggestionsforaltering Procurement policycan throughunilateralstrategies. payoffstructures i8 Haas, Williams, and Babai, Scientists and WorldOrder:The Usesof TechnicalKnowledge in InternationalOrganizations(Berkeley:Universityof CaliforniaPress, I977). 10 WORLD POLITICS affectthe prospectsforcooperation. If one superpowerfavorsprocurementof defensiveoveroffensive weapons,it can reduceitsown gains fromexploitation through surprise attack(DC) and reduceitsadversarys fearof exploitation (CD). Membersof allianceshave oftenresortedto the device of deployingtroopson troubledfrontiers to increasethe likelihoodofcooperation. A statesuse of troopsas hostagesis designed to diminishthepayoff fromitsown defection-toreduceitsgainsfrom exploitation (DC)-and thereby renderdefensive defection byitspartner lesslikely.Publicizingan agreement

diminishes payoffs associatedwith defectionfromthe agreement, and therebylessensgains fromexploiin international tation.These observations relationsare paralleledby recentdevelopments in microeconomics. OliverWilliamsonhas identifiedunilateraland bilateraltechniquesusedbyfirmsto facilitate interfirmcooperationby diminishinggains fromexploitation. He distinguishesbetweenspecificand nonspecific costsassociatedwithadherence to agreements. machinetools, Specificcosts,suchas specializedtraining, and construction, cannotbe recoveredin the eventof the breakdown ofan agreement. Whenpartiestoan agreement incurhighspecific costs, repudiation ofcommitments willentailsubstantial losses.Firmscan thus reducetheirgainsfromexploitation throughthetechniqueofacquiring dedicatedassetsthatserveas hostagesto continuing Noncooperation. specificassets,such as general-purpose trucksand airplanes,are salvageableifagreements breakdown;firmscan reducetheirfearofbeing exploitedby maximizingthe use of nonspecific

assets,but such assets cannotdiminishgains fromexploitation Uniby servingas hostages.9 lateral strategiescan improve the prospectsof cooperationby reducing both the costs of being exploited (CD) and the gains fromexploitation (DC). The new literatureon interfirmcooperationindirectlyraises an old question on the costs of unilateralstrategiesto promotecooperation in internationalrelations. In many instances,unilateral actions that limit ones gains from exploitation may have the effectof increasingones vulnerabilityto exploitationby 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 unquestionablyincrease the credibilityof the nations commitmentto liberalism.It also I9Williamson(fn.5). EXPLAINING COOPERATION UNDER ANARCHY 11

to prohowever,of increasingthenationsvulnerability has theeffect, that example,thegovernment tectionbyothers.In thetroops-as-hostage an allysfear stationstroopsmay promotecooperationby diminishing but in so doingit raisesitsown fearsof exploitation of abandonment, nuclearliterature, by theally.In an examplefromtheneoconservative and others assumethat Gray, William Van Cleave, Paul Nitze, Colin or missileswill be firedagainstmissilesratherthanagainstindustries towardcountervalue cities,and concludethata shiftfromcounterforce at the weaponsmay purchasea reductionin gains fromexploitation Cognitive,domesvulnerability to exploitation.2o expenseof heightened directly, structural factorsaffectpayoffstructure tic,and international of the benefitsand limitsof unilateral and also influenceperceptions to alterpayoffs. strategies do not exhaustthe rangeof optionsthatstates Unilateralstrategies Bilateralstrategies-most structures. significantly mayuse toalterpayoff by strategiesof issue

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linkage-can be used to alterpayoffstructures combiningdissimilargames. Because resortto issue linkagegenerally assumesiteration,analysisof how issue linkagecan be used to alter payoffsis presentedin the sectionon the shadowof the future.Furthermore, can aim at alteringanother strategies bilateral"instructional" of cause-and-effect relationships, and resultin understanding countrys in of interest.For example,Americannegotiators alteredperceptions SALT I soughtto instructtheirSovietcounterparts on the logic of mutual assured destruction.21 Multilateral strategies,centeringon the formationof international regimes,can be used to alter payoffstructuresin two ways. First,norms generated by regimes may be internalizedby 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 See Paul Nitze, "AssuringStrategicStabilityin an Era of Detente," ForeignAffairs54 (JanuaryI976), 207-32, for the seminal article in this tradition.Nitzes recommendations hinge on acceptance of the preceptsof what has come to be known as nuclear utilization theory.Jervissrecommendationsdepend on acceptanceof the preceptsof mutual assured destruction(fn. 5). 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). 20 21 12 WORLD III. POLITICS THE SHADOW OF THE FUTURE: SINGLE-PLAY AND ITERATED GAMES The distinction betweencases in whichsimilartransactions among partiesare unlikelyto be repeatedand cases in whichtheexpectation offutureinteraction caninfluence decisionsinthepresent is fundamental to

theemergenceofcooperation amongegotists. As theprevioussection statesconfronting suggests, strategic situations thatresemblesingle-play PrisonersDilemma and, to a lesserextent,single-play Stag Hunt and Chicken,are constantly temptedby immediategains fromunilateral and fearful ofimmediatelossesfromunrequitedcooperation. defection, How does continuing interaction affectprospects forcooperation? The argumentproceedsin fourstages.First,why do iteratedconditions improvetheprospectsforcooperationin PrisonersDilemmaand Stag Hunt whilediminishing theprospects forcooperation in Chicken?Second, how do strategiesof reciprocity improvethe prospectsfor cooperationunderiteratedconditions?Third,whydoes theeffectiveness of reciprocity hingeon conditionsof play-the abilityof actorsto distinguishreliablybetweencooperationand defectionby othersand to respondin kind? Fourth,throughwhat strategies can statesimprove conditionsof playand lengthentheshadowof thefuture?23 Beforeturningto

thesequestions,considertheattributes of iterated situations. First,statesmustexpectto continuedealingwitheach other. This conditionis, in practice, notparticularly Withtheposrestrictive. sible exceptionof global thermonuclear war, international politicsis characterizedby the expectatonof futureinteraction. Second,payoff structures mustnotchangesubstantially overtime.In otherwords,each roundof playshouldnotalterthestructure of thegame in thefuture. This conditionis, in practice, quiterestrictive. For example,statesconattack when offense is dominantare in a situationthat sideringsurprise hasmanyofthecharacteristics ofa single-play game:attackaltersoptions and payoffs in futureroundsof interaction. nationsconsidConversely, eringincreasesor decreasesin theirmilitary budgetsare in a situation thathasmanyofthecharacteristics ofan iterated game:spendingoptions and associatedmarginalincreasesor decreasesin military are strength likelyto remainfairlystableover futureroundsof interaction. In

internationalmonetaryaffairs,governments consideringor fearingdevaluationunder a gold-exchangestandardare in a situationthathas of a single-play manyof the characteristics game: devaluationmaydiminishthe value of anotherstatesforeigncurrency reserveson a one23 This sectionis derived largelyfromAxelrod (fn. 7), and Telsor (fn. 6). EXPLAINING COOPERATION UNDER ANARCHY 13 time basis, while reductionsin holdingsof reserveswould diminish considering governments possiblelosseson a one-timebasis.Conversely, under a floatingsystemwith minimalreservesare in a intervention of an iteratedgame: desituationthathas manyof the characteristics would not producesubstantial of a currency preciationor appreciation one-timelossesor gains.Third,thesize of thediscountrateappliedto placeslittle ofgames.If a government thefutureaffects theiterativeness of itssituationhas manyof thecharacteristics value on futurepayoffs, payoffs, itssituation a single-play game.If itplacesa highvalueon future ofan

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iteratedgame.For example, mayhavemanyof thecharacteristics politicalleadersin theirfinaltermare likelytodiscountthefuturemore thanpoliticalleadersrunningfor,or certainof,reelection. substantially A. THE SHADOW OF THE FUTURE AND COOPERATION How does the shadowof the futureaffectthelikelihoodof cooperadherenceto conditionswithouta sovereign, ation?Under single-play PrisonersDiagreementsis oftenirrational.Considerthe single-play lemma.Each prisoneris betteroffsquealing,whetheror nothispartner defection decidesto squeal. In the absenceof continuinginteraction, the can neiBecause prisoners would emergeas thedominantstrategy. of an agreementto forenforcement therturnto a centralauthority cooperatenor relyon the anticipationof retaliationto deterpresent conditions.If defection, cooperationwill be unlikelyundersingle-play in thefuture, the theprisoners expectto be placedin similarsituations evidencesuggeststhat forcooperation improve.Experimental prospects underiteratedPrisonersDilemma

the incidenceof cooperationrises tacitagreeEven in theabsenceof centralizedauthority, substantially.24 reached are frequently mentsto cooperatethroughmutualstonewalling a defector and maintained. UnderiteratedPrisoners Dilemma, potential comparestheimmediategain fromsquealingwiththepossiblesacrifice In single-playStag of futuregains thatmay resultfromsquealing.25 24 See Anatol Rapoportand AlbertChammah,Prisoners Dilemma (Ann Arbor:University of Michigan Press, i965), and subsequentessaysin Journalof ConflictResolution. 25 One commonobjectionto thisline ofargumentcenterson theirrationality ofcooperation if a sequence of PrisonersDilemmas 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 bothactorsknow thatcooperationis irrationalon the last move. And so on back toward the initialmove. This

line of analysiscollapses iteratedPrisoners Dilemma into single-playPrisonersDilemma. To analystsof internationalrelations,the importanceof this objection is limited.In internationalrelations,no experimenterdecrees thata series of PrisonersDilemmas shall end on the ioth move or at noon. Althoughany series of transactionswill terminatesooner or later,governmentsdo not generallyknow when the last play will occur. On all rounds of play, the actors decisionsare conditioned 14 WORLD POLITICS Hunt, each hunteris temptedto defectin orderto defendhimselfagainst the possibilityof defectionby others. A reputationfor reliability,for resistingtemptation,reduces the likelihood of defection.If the hunters are a permanentgroup,and expectto hunttogetheragain, the immediate gains fromunilateraldefectionrelativeto unrequited cooperationmust be balanced against the cost of diminishedcooperationin the future.In both Prisoners Dilemma and Stag Hunt, defection in the present decreasesthe likelihood of

cooperationin the future.In both, therefore, iterationimprovesthe prospectsforcooperation.26In Chicken, iteration may decrease theprospectsforcooperation.Under single-playconditions, the temptationof unilateral defection is balanced by the fear of the collision that follows frommutual defection.How does iterationaffect then each drivermay this balance? If the game is repeated indefinitely, refrainfrom 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 otherdriverto swerve.In iteratedChicken, one driversdefectionin the presentmay decrease the likelihood of the other drivers 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 cooperationin the illustrationsabove, an iteratedenvironment permits resort to

strategiesof reciprocitythat may improve the prospectsof cooperation in Chicken as well as in Prisoners Dilemma and Stag Hunt. RobertAxelrod argues thatstrategiesof reciprocityhave the effectof promotingcooperationby establishinga direct connection between an actors presentbehaviorand anticipatedfuturebenefits.Titfor-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 formalanalysisof how uncertaintimehorizons can lead to a resolutionof the PrisonersDilemma, see Luce and Raiffa(fn. 6), Appendix Possible 8. Discount parameterssuch as Axelrods"w" maycapturetheeffectsof uncertainty. futurepayoffsmay be discountedboth because the value placed on futurebenefitsis lower than presentbenefitsand because the streamof futurebenefitsmay be interruptedif the structureof the game changes. This conclusion restson the assumptionthat dyadic

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interactionsare moderatelyindependent.For an argumenton how defectioncan providea benefit(externalto 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 thatcooperationcan also encourage (mutuallybeneficial) entryof otheractors. On iteratedChicken, see Snyderand Diesing (fn. 4), 43-44. 26 27 EXPLAINING COOPERATION UNDER ANARCHY 15 In iterated Prisoners Dilemma and Stag Hunt, reciprocityunderscoresthe futureconsequences of presentcooperationand defection.The argument presented above-that iterationenhances the prospects for cooperationin 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

cooperativehuntingwith cooperativehuntingvalidates the assumption. In iteratedChicken, a strategyof reciprocitycan offsetthe perverseeffectsof reputationalconsiderationson the prospectsfor cooperation.Recall that in iteratedChicken, each drivermay refrainfrom swervingin the presentto coerce the other driverinto swervingin the future. Adoption of an implicit or explicit strategyof Tit-for-Tat in iteratedgames of Chicken altersthe futurestreamof benefitsassociated with presentdefection.If a strategyof reciprocityis credible,then the mutual losses associated with futurecollisions can encourage present swerving.In all threegames, a promiseto respondto presentcooperation with future cooperation and a threat to respond to present defection with futuredefectioncan improve the prospectsfor cooperation. The effectivenessof strategiesof reciprocityhinges on conditionsof play-the ability of actors to distinguishreliablybetween cooperation and defection by others and to respond in kind. In the

illustrations provided above, the meaning of "defect" and "cooperate" is unambiguous. 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 actorseliminatesthe possibilityof controlproblems. Unitary prisoners,hunters,and drivers do not sufferfrom factional, organizational, or bureaucraticdysfunctionsthat might hinder implementationof strategiesof reciprocity. In internationalrelations,conditionsof play can limitthe effectiveness of reciprocity.The definitionof cooperationand defectionmay be ambiguous. For example, the Soviet Union and the United States hold to markedlydifferentdefinitionsof "defection"fromthe termsof detente as presented in the Basic

Principles Agreement;28the European Community and the United States differover whether domestic sectoral policies comprise indirectexportsubsidies. Further,actions may not be 28 See Alexander L. George, Managing U.S.-SovietRivalry:Problemsof CrisisPrevention (Boulder, CO: Westview, i983). 16 WORLD POLITICS For example,governments transparent. maynot be able to detectone or indirectexportsubanothersviolationsof armscontrolagreements sidies. If defectioncannotbe reliablydetected,the effectof present willerode.Together,ambiguous cooperation on possiblefuturereprisals can limittheabilityof statesto and a lack of transparency definitions recognizecooperationand defection byothers. controlis as important as recBecausereciprocity requiresflexibility, and bureaucratic ognition.Internalfactional,organizational, dysfuncTit-for-Tat tionsmaylimittheabilityofnationstoimplement strategies. lineofpolicythantosella strategy It maybe easierto sellone unvarying of shifting betweenlinesof policyin

responseto theactionsof others. For example,arms suppliersand defenseplannerstend to resistthe of weaponssystems cancellation evenifthecancellation is a responseto industriestend to resistthe the actionsof a rival.Import-competing removalofbarriersto imports, eveniftradeliberalization is in response to liberalizationby anotherstate.At times,nationaldecisionmakers ofreciprocity. On otheroccasions, maybe unableto implement strategies For thesereasons,national theymustinvestheavilyin sellingreciprocity. decisonmakersmay displaya bias againstconditionalstrategies:the offset thevalue domesticcostsof pursuingsuchstrategies maypartially thatconditionalpoliciesare of thediscountedstreamof futurebenefits expectedto yield. As RobertAxelrodnotes,problemsof recognition and controlmay In thissymposium, such problems limiteffective resortto reciprocity. are examinedin severalways. The essay on "Arms Races and Coa simplesimulation operation"presents designedtoassessthesensitivity of

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Tit-for-Tatstrategiesto departuresfromperfectrecognition and control.The case studiesand theconclusionassesstheextentto which and controlare, in practice,impediments to problemsof recognition effective utilizationof strategies of reciprocity.29 C. STRATEGIES OF THE TO IMPROVE RECOGNITION AND LENGTHEN THE SHADOW FUTURE To what extentcan governments promotecooperationby creating the shadow of the favorableconditionsof play and by lengthening severaltechniques future?The literature on international regimesoffers of norms forcreatingfavorableconditions of play.Explicitcodification 29 Axelrod shows thatin iterated PrisonersDilemma, whereactorscan reliablydistinguish between cooperation and defectionby othersand respond in kind, Tit-for-Tatperforms betterthan do alternativestrategies.When recognitionand control are perfect,iterated environmentsstronglyfavorthe emergenceof cooperation. EXPLAINING COOPERATION UNDER ANARCHY 17 standardsof ambiguity. The veryactofclarifying can

limitdefinitional and uncooperative behavior, can permit cooperative conduct,ofdefining of reciprocity. for Further,provisions moreeffective resortto strategies forverification in armscontrol surveillance-forexample,mechanisms on the natureand effectsof agreementsor for sharinginformation In practice,the domesticsectoralpolicies-can increasetransparency. is oftencentralto negotiations capabilities goal ofenhancingrecognition underanarchy. offer literatures and institutional microeconomic The game-theoretic severalapproachesto increasingthe iterativecharacterof situations. Thomas Schellingand RobertAxelrodsuggesttacticsof decomposition For example,the over time to lengthenthe shadow of the future.30 billiondollarsfora billion thirty to defectin a deal promising temptation barrelsof oil may be reducedif the deal is slicedup intoa seriesof or in territorial and deliveries. Cooperationin armsreduction payments ifthereduction or disengagement must disengagement maybe difficult or

disengagement can be sliced be achievedin one jump.If a reduction theproblemof cooperation maybe renderedmore up intoincrements, of issuelinkagecan be used to alterpayoff tractable. Finally,strategies intosingle-play sitstructures and to interject elementsof iterativeness issue uations.Relationsamongstatesarerarelylimitedtoone single-play a single-play ofoverriding Whennationsconfront gameon importance. on maybe deterredbythreatsof retaliation one issue,presentdefection otheriteratedissues.In international monetary affairs,forinstance,a government fearingone-timereservelossesifanotherstatedevaluesits tradegame.Byestablishing currency maylinkdevaluationtoan iterated a directconnection gameand betweenpresentbehaviorin a single-play in an iteratedgame,tacitor explicitcross-issue linkage futurebenefits can lengthentheshadowof thefuture.3 of reciprocity, and payoffstrucThe shadowof thefuture, strategies to Incentives tureinteract in determining thelikelihoodofcooperation. payoffs

cooperateand to defectare thediscountedstreamofanticipated The sizeofthediscountrateaffects acrosscurrent and future encounters. A Tit-for-Tatstrategy the value of futurebenefits. providesa clearer future view of how presentbehavioris likelyto affectan adversarys betweenthe anticipated behavior,and therebysharpensdifferences Schelling (fn. 2), 43-46,and Axelrod (fn. 7), i26-32. For analyses of issue linkage, see Robert D. Tollison and Thomas D. Willett, "An Economic Theory of MutuallyAdvantageousIssue Linkages in InternationalNegotiations," International Organization33 (Autumn I979) 425-49; Oye (fn. i2), chap. 3, "Bargaining:The Logic of ContingentAction"; and Axelrod and Keohane in the concluding essay of this symposium. 3- 3 WORLD POLITICS 18 streamof payoffsforcooperationand 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 payoffstructureand the shadow of the futureon the prospectsof cooperation in termsof twoperson situations.What happens to the prospectsforcooperationas the number of significantactors rises? In this section, I explain why the prospectsfor cooperation diminish as the number of players increases; examine the functionof internationalregimesas a responseto the problems created by large numbers; and offer strategiesto improve the prospectsfor cooperationby alteringsituationsto diminishthe number of significantplayers. The numbers problem is centralto many areas of the social sciences. Mancur Olsons theoryof collectiveaction focuseson N-person versions of Prisoners Dilemma. The optimismof our earlier discussionsof cooperationunder iteratedPrisonersDilemma gives way to the pessimism of analyses of cooperationin the provisionof public goods. Applications of Olsonian theoryto problems ranging fromcartelizationto the provision of public goods in alliances underscorethe

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significanceof "freeriding" as an impediment to cooperation.32In internationalrelations, the numbersproblem has been centralto two debates.The longstanding controversyover thestabilityofbipolarversusmultipolarsystemsreduces to a debate over the impact of the number of significantactors on between proponents A more recentcontroversy, internationalconflict.33 of the theoryof hegemonic stabilityand advocates of internationalregimes, reduces to a debate over the effectsof large numbers on the robustnessof cooperation.34 See Mancur Olson, Jr.,The Logic of CollectiveAction:Public Goodsand 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 collectiveaction, see Russell Hardin, CollectiveAction (Baltimore: Johns Hopkins UniversityPress, i982). 33See

Kenneth N. Waltz, "The Stabilityof a Bipolar World," Daedalus 93 (Summer and the Future,"Journalof i964), and Richard N. Rosecrance,"Bipolarity,Multipolarity, ConflictResolution(September I966), 3 14-27. (New 34On hegemony,see Robert Gilpin, U.S. Power and theMultinationalCorporation York: Basic Books, I975), 258-59. On duopoly,see TimothyMcKeown, "Hegemonic Stability Theory and i9th-CenturyTariffLevels in Europe," InternationalOrganization37 (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,"Dominance and Leadership in the InternationalEconomy: Exploitation,Public Goods, and Free StudiesQuarterly25 (June i98i), 242-54. Rides," International 32 EXPLAINING A. NUMBER OF PLAYERS COOPERATION AND UNDER ANARCHY 19 COOPERATION How do numbersaffectthelikelihoodof cooperation?There are at leastthreeimportant channelsof

influence.35 requires First,cooperation as recognition ofopportunities fortheadvancement ofmutualinterests, wellas policycoordination oncetheseopportunities havebeenidentified. and information costs As the numberof playersincreases,transactions rise.In simpleterms,the complexity of N-personsituationsmilitates and realizationof commoninterests.Avoiding againstidentification nuclearwar duringthe Cuban missilecrisiscalled forcooperationby theSovietUnionand theUnitedStates.The transaction and information costsin thisparticularly did not harrowingcrisis,thoughsubstantial, theproblemofidentifying significant precludecooperation. Bycontrast, actors,defininginterests, and negotiating agreementsthatembodied in theN-actorcaseof I9I4 was farmoredifficult. These mutualinterests secondarycostsassociatedwithattainingcooperativeoutcomesin Nactorcaseserodethedifference betweenCC and DD. Moresignificantly, theintrinsic of anticipating difficulty thebehaviorof otherplayersand

ofweighingthevalueofthefuturegoesup withthenumberofplayers. The complexity ofsolvingN-persongames,evenin thepurelydeductive sense,has stuntedthe developmentof formalwork on the problem. This complexity is even greaterin real situations, and operatesagainst multilateral cooperation. Second,as the numberof playersincreases,thelikelihoodof autonomous defectionand of recognition and controlproblemsincreases. ofexpectedutility-merging Cooperativebehaviorrestson calculations discountrates,payoffstructures, and anticipated behaviorofotherplayers.Discountratesand approachesto calculation are likelyto varyacross actors,and the prospectsformutualcooperationmay declineas the numberof playersand the probableheterogeneity of actorsincreases. The chancesof includinga statethatdiscountsthefutureheavily,that is too weak (domestically) of to detect,react,or implementa strategy thatcannotdistinguishreliablybetweencooperationand reciprocity, defection by otherstates,or thatdepartsfromevenminimalstandards

ofrationality increasewiththenumberofstatesin a game.For example, manypessimistic analysesof the consequencesof nuclearproliferation focuson how breakdownsofdeterrence maybecomemorelikelyas the numberof countrieswithnuclearweaponsincreases.36 thefeasibility ofsanctioning Third,as thenumberofplayersincreases, to defectors diminishes.Strategies of reciprocity becomemoredifficult 35See Keohane (fn. ii), chap. 6, forextensionsof these points. 36 See Lewis A. Dunn, Controlling theBomb (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 sanctioningdefectorscreates the possibility of free-riding.What happens if we increasethe number of actorsin the iterated Prisoners Dilemma from 2

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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 equivalent of retaliationagainst all. In N-person games, a strategyof conditional defectioncan have the effectof spreading,ratherthan containing, defection. B. STRATEGIES OF INSTITUTIONALIZATION AND DECOMPOSITION Given a large number of players,what strategiescan states use to increasethe likelihood of cooperation?Regime creationcan increasethe likelihoodof cooperationin N-persongames.37First,conventionsprovide rules of thumb that can diminish transactionand informationcosts. Second, collectiveenforcementmechanismsbothdecrease the likelihood of autonomous defectionand permit selectivepunishmentof violators

of norms. These two functionsof internationalregimesdirectlyaddress problems created by large numbersof 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 theirassessmentof the militaryvalue of some goods and technologies, there is consensus on a ratherlengthylist of prohibiteditems. By facilitatingagreementon the prohibitedlist,the CoordinatingCommitteeof the Consultative Group of NATO (CoCom) provides a relatively 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.38 Generally,cooper37 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 Relationswith 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 modificationthroughregimiststrategies. What strategiescan reduce the number of significantplayers in a game and therebyrendercooperationmore likely? When governments are unable to cooperateon a global scale,theyoftenturnto discriminatory strategiesto encourage bilateralor regional cooperation.Tactics of

decompositionacross actors can, at times, improve the prospectsfor cooperation. Both the possibilitiesand the limits of strategiesto reduce the number of playersare 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 bilateralclearingarrangementis less economicallyefficient than a multilateralclearingarrangement.Strategiesto reduce the numberof players in a game generally diminish the gains from cooperation while they increasethe likelihoodand robustnessof cooperation.39 Second, strategies to reduce the number of playersgenerallyimpose substantialcosts on third parties. These externalitiesmay motivatethird parties to undermine the limited area of cooperationor may serve as an impetus for a thirdpartyto enlarge the zone of cooperation.In the I930s, forexample, wholesale resortto

discriminatorytradingpolicies facilitatedcreationof exclusive zones of commercialopenness. When confrontedby a shrinking 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 marketshare diminished,the United States adopted a more liberal and more discriminatorycommercial policy to increaseitsaccess 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 thenumberof actorsin a tradewar,market access can simply be offeredto only one countryand withheld from others.By contrast,defectionby only one suppliercan permitthe target Union," WorldPolitics37 (Julyi985), 503-3I, and BeverlyCrawfordand StephanieLenway, "Decision Modes and InternationalRegime Change:

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WesternCollaborationon East-West Trade, WorldPolitics37 (April i985), 375-402. 39 For a pure libertarianargumenton privateexchange as an alternativeto public management,see Conybeare (fn. i2). 22 WORLD POLITICS of a strategicembargo to obtain a criticaltechnology.These problems may limit the range of situationssusceptibleto modificationthrough strategiesthat reduce the number of playersin games. IV. CONCLUSION As I noted at the outset, the analytic approach presented in this symposium constitutesan implicit attack on the traditionalboundary betweenstudiesof internationalpoliticaleconomyand studiesof security. The emphasis on cooperation,the reliance on the three circumstantial dimensions,and theanalysisofassociatedstrategiesto altercircumstances are not specificto eithersecurityaffairsor politicaleconomy.This essay and Duncan Snidals complementaryintroduction,"The Game Theory of International Politics," define and operationalize the three sets of abstractexplanatoryand

prescriptivepropositions,and discuss the uses and abuses of game theoryin theempiricalstudyof internationalpolitics. The six empirical essays in the main body of this collection provide a limitedtrialof thesepropositionsbyprobingdiversesituations,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 durationof great-powerconcerts.He begins by noting that counterhegemonicwar appears to be a necessary condition for the emergenceof concert,and then offersan explanation of why the Concert of Europe lasted from i8I5 to i854, but attempts at concertfollowingWorld Wars I and II collapsed. His analysisstresses the effects of an international structural cause-counterhegemonic war-and of concertitselfon the preconditionsfor cooperation. Stephen Van Evera explains the collapse of a fragilepeace in I9I4. His analysis stressesthe effectsof a familyof ideas-militarism, nationalism,and

social imperialism-on the governingelites perceptions of theirinterestsand of each other.Van Evera suggeststhat these ideas underminedeach of the threesituationalpreconditionsforcooperation, and are necessaryto the explanationof the outbreakof the First World War. George Downs, David Rocke, and Randolph Siversontranscendsome of the superficialcontroversiesover strategythatdivide analystsof arms control.Their essay identifiesconditionsthatdeterminewhen unilateral 4 See AlexanderGeorge and RichardSmoke,Deterrencein AmericanForeignPolicy(New York: Columbia UniversityPress, I974) fora seminalexample of how an austeretheoretical frameworkand detailed historicalcases can promote both development of theoryand historicalunderstanding. EXPLAINING COOPERATION UNDER ANARCHY 23 action, tacitbargaining,and explicitnegotiationare likelyto 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,JohnConybeare examines factorsthatmay promoteand inhibitcommercialcooperation. He explains why cooperation was not robust during the perpetual iterationsof 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, internationalmonetaryrelationswere marked by the collapse of fixedexchange rates and resortto competitivedevaluation,the emergenceof bilateraland regionalcooperation,and limited monetarycoordination under the Tripartite Stabilization Agreement. Kenneth Oye considerscircumstantialand strategicdeterminantsof the incidence and scope of monetarycooperationin the I930s. In timesof financialcrisis,individualcreditorscan derivebenefitfrom limitingtheirexposureto

protectthemselvesagainstdefault.But ifmany 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 institutionalsettingshave fosteredcooperation(to date). By juxtaposing a generic analytic frameworkand two sets of cases organized along traditionalsubdisciplinaryboundaries,the contributors to thiscollectionencourage speculationalong severallines. First,to what extentdo cases in securityaffairsand politicaleconomytend to fall into differentareas of the space definedby the threesituationaldimensions? Second, to what extent does readiness to resort to associated sets of strategiesappear to differin securityaffairsand political economy? Third, what aspects of cooperationin securityaffairsand politicaleconomy are not explained by the core approach employed in this volume? Finally,what additionalsituationaland

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strategicvariablesmightimprove the quality of explanation? In the concludingessay,RobertAxelrod and RobertKeohane consider these questions. They begin by examining the fit between observed cooperationand conflict,and the threesets of situationalpreconditions. They then review the case studies,assessing the possibilitiesand limits of strategiesto alter payoffstructure,to lengthen the shadow of the futureand create favorableconditionsof play, and to reduce numbers 24 WORLD POLITICS ofplayers,withparticular emphasison reciprocity and regimebuilding. Axelrodand Keohane ultimately move towarda new synthesis. They suggestthatinternational regimescan reinforce and institutionalize recand thatnationshave enhancedtheprospectsforcooperation iprocity, by relyingon a combination of atomisticreciprocity and regimeestablishment.