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Absolute and Relative Gains in International Relations Theory

Author(s): Robert PowellSource: The American Political Science Review, Vol. 85, No. 4 (Dec., 1991), pp. 1303-1320Published by: American Political Science AssociationStable URL: http://www.jstor.org/stable/1963947 .

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ABSOLUTEAND RELATIVEGAINS IN INTERNATIONALRELATIONSTHEORYROBERTPOWELLUniversityof CaliforniaBerkeley

he problem of absoluteand relativegains divides neoliberal nstitutionalismand structural ealism.The ormerassumes tatesfocus primarily n theirabsolutegainsandemphasizesheprospects or cooperation.The latter upposesstates are largelycon-cerned with relativegains and emphasizes he prospects or conflict. Existingwork ininternational elations heorygenerally races hedifferencesbetween hese two theoriesto differentassumptions bout states'preferences.Usinga simplegame-theoreticmodel,thisessay offersa reformulation f theproblemof absoluteandrelativegains that linkschanges n thestates'behavior,thefeasibilityof cooperation,and especially he states'concern or relativeversus absolutegains explicitlyto changes n the constraints acingthe states. Many of the differencesbetween neoliberal nstitutionalism nd structuralrealismappearas special cases of the model.

lrhe problemof absoluteandrela-tive gains divides two of the most influ-ential approachesto internationalrela-tions theory. Neoliberalinstitutionalismassumes that states focus primarilyontheir individual absolute gains and areindifferent o thegainsof others.Whethercooperationresultsin a relative gain orloss is not very importantto a state inneoliberalinstitutionalism o long as itbringsan absolutegain. In termsof pref-erences, this focus on absolute gains isusuallytaken to meanthata state'sutilityis solely a functionof its absolutegain. Incontrast,neorealism,orstructural ealismassumes hat statesare largelyconcernedwith relativerather than absolute gains.In the anarchy of internationalpolitics,"relative gain is more important thanabsolutegain" Waltz1959, 198).A state'sutilityinstructural ealism s at leastpart-ly a functionof somerelativemeasure ikepower.1 These differing assumptions

about states'preferences ead to differentexpectations bout the prospects or inter-national conflict and cooperation. Themore states careaboutrelativegains, themore a gain for one state will tend to beseen as a loss by anotherand the moredif-ficult, it seems, cooperationwill be.2However,tracingdifferent xpectationsabout the likelihoodof conflict and coop-eration to different assumptionsaboutstates' preferencesposes an importanttheoretical difficulty for internationalrelations theory.3Jervis (1988), Keohane(1984), Lipson(1984), Stein (1983, 1984),and the contributors o the volumeeditedby Oye (1986) have recently called fortryingto bringat least some aspectsof thestudy of internationalpoliticaleconomy,whichis usually takento be the provinceof neoliberal institutionalism,and thestudyof securityaffairs,whichis usuallytaken to be the province of structuralrealism, within a single analytic frame-

AMERICAN POLITICAL SCIENCEREVIEWVOLUME 85 NO. 4 DECEMBER1991

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AmericanPoliticalScienceReview Vol. 85work. But if neoliberal institutionalismand structural ealismreallydomakefun-damentallydifferentassumptionsaboutstates' preferences, hen efforts to unifythese approacheswith a third-imageex-planationcannotsucceed.To use Waltz'sanalogy (1979, 89-91)betweenpoliticalstructures nd economicmarketstructures,t will be impossible oexplainthedifferencesbetweenneoliberalinstitutionalismand structural realismover, say, the prospectsfor internationalcooperation n the same way that econo-mistsexplainthe differencesbetweenout-comes in a perfectlycompetitive marketand a monopoly. In that explanation,economists assume that the goals orpreferencesof the unit, in this case thefirm, are the same in both a perfectlycompetitivemarketandin a monopoly:afirm seeks to maximize ts profits.Whatvaries in movingfrom one marketstruc-tureto theother are theconstraintsunderwhich a firm attempts to maximizeitsprofits. Thus, changes n the marketcon-straints and not in the units' preferencesaccount for the variation in a firm'sbehavior in the two different marketstructures. f, however,neoliberalnstitu-tionalism and structural realism areactuallybasedon fundamentally ifferentassumptions about states' preferences,then moving from a neoliberal institu-tional to a structural ealistsettingwouldsee a change in the attributesof states,that is, their preferences.In this sense,neoliberal nstitutionalismand structuralrealism would be about essentiallydif-ferenttypes of units, one primarilycon-cernedwith absolutegains,the otherwithrelativegains.Consequently, he locus ofthe differencesbetween neoliberal nstitu-tional and structuralrealistexplanationsof internationalbehaviorwouldbe in thefirstor secondimages.A third-image ni-ficationof these approaches,which wouldexplain changes in states' behavior intermsof changes n the constraints acingthe states and not in termsof changes n

the type or nature of states'preferences,would be impossible.I offer a reformulationof the problemof absolute and relativegainsand takeasteptoward bringing hestudyof interna-tional conflict and cooperationwithin asingle analytic framework.4 show thatmany important aspects of neoliberalinstitutionalism and structural realismmaybe seenas specialcasesof a verysim-ple model of the international ystem inwhichchanges n the states'behavior, the

feasibilityof cooperation, and especiallythe states' concern for relative versusabsolutegainsareexplicitly inked not todifferent assumptionsabout the states'preferencesbut to changes in the con-straints acingthe states.The model thusshifts the focus of analysis away frompreferences o constraints.5In the model, statesare assumedto betrying to maximizetheir absolute gains.That is, a state'sutilitydependssolely onthe absolutelevel of economicwelfare itattains. This is in keepingwith neoliberalinstitutionalism.But the statesare tryingto maximize their economic welfarewithin the constraints imposed by ananarchic internationalsystem in whichtheuseof force,inkeepingwith structuralrealism,may be at issue. When the costofusingforceis sufficientlyow thatthe useof force actually is at issue, cooperativeoutcomes that offer unequal absolutegains cannot be supportedas part of anequilibrium ven thoughthe states'pref-erencesare definedonly over theirabso-lute level of economic welfare. This in-abilityto cooperate s in accord with theexpectationsof strucural ealism, thoughtheassumption hat states aremaximizingtheir absolutegainsis not in keepingwithits usualformulations.If the use of forceis not at issuebecause ighting s too cost-ly, then the results are more in accordwith neoliberal institutionalism. Forexample, cooperative outcomes thatcould not be sustained when the use offorce was at issue now become feasible.

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InternationalRelationsTheoryThus, many aspectsof neoliberal nstitu-tionalismandstructural ealismappearasspecialcasesof the model.Themodeldevelopedbelowis extreme-ly simple. It aimsprimarilyat conceptualclarification, not empirical application.To this end, it has been deliberatelydesigned o show, in the simplestpossiblewell-definedgame-theoreticmodel, thatmany of the differencesbetween neo-liberal institutionalism and structuralrealismcanbe tracedexplicitly o thecon-straints acingstates, ratherthanto theirpreferences.Theextreme implicityof themodel clarifiesthe relationbetween con-straintsand the problemof absolute andrelative gains that although present inmorecomplicatedmodels, wouldbe moredifficult to discern there. The develop-ment of more complicatedand less con-trived models awaits future work.6 Butdespitethe model'ssimplicity, ts analysismakes threenew points that are relevantto internationalrelations theory. Mostnarrowly,it suggeststhat cooperation nsome circumstancesmay be even moredifficult to achieve than has been pre-viously appreciated. Some agreementsthat offer equal absolute gains-andthereforeno relativegain-cannot be sus-tained in equilibrium.The reasonis thatcheating on the agreementwould bringlargerelativegains.The second and third points addresstwo otherbroader ssues in internationalrelationstheory. Themodel offers a sim-ple formalexampleshowingthat Waltz'snotion of political structure s unabletoaccount or important hanges n the feas-ibility of internationalcooperation.Thepolitical structure as Waltz defines it(1979,79-101) remainsconstantthrough-out the analysis; but the feasibility ofcooperation varies. Thus, variations inwhat Waltztakes to be thestructure f thepoliticalsystemcannotexplain the varia-tionin thefeasibilityof cooperation nthemodel.The second ssue is therelationbetween

anarchyandcooperation.Structural eal-ism generallyassociatesanarchywith aconcernfor relativegains and a lack ofcooperation Waltz1979,105).Neoliberalinstitutionalism, however, argues thatanarchy n the sense of a "lackof a com-mon government"AxelrodandKeohane1986, 226; Keohane 1984, 7) does notimply a lack of cooperation (Keohane1984, 65-84). The presentanalysishelpsto elucidate he sourcesof thisdifference.Theability or inabilityto enforcerulesofbehavioris relevantonly if the physicalenvironmentdefinedby the system'scon-straintsis such that one of the possiblebehaviors is to use one's relativegain toone's advantageand to the disadvantageof others.If thereareno suchopportuni-ties, then the inability to commitoneselfto a promisenot to use a relativegain toone's advantage s moot. Thus, the con-cern for relativegains arises from bothanarchy and the constraints that definethe rangeof possiblebehavior.Althoughsuch a system is clearlyimplicit n struc-tural realism, neither neoliberal institu-tionalism nor structural realism fullyappreciatesthe significanceof the sys-tem'sconstraints n theoriginsof thecon-cern for relativegains.One consequenceof the failureof bothstructuralrealismand neoliberal nstitu-tionalism to appreciate the role of thesystem's constraints in the problem ofabsolute and relative gains is the useof repeatedgames in both of these ap-proachesto model the international ys-tem implicit in structuralrealism (e.g.,Jervis 1978, 171; Keohane 1984; Oye1986).As will be shown, relativegainsinrepeatedgames, including the repeatedprisoner'sdilemma, cannot be used toone's advantage.Thus, even if statesareunable to make binding agreementsinthese models, relative gains in repeatedgames do not matter. This rendersanyanalysis of structural realism's under-standingof therelationbetweenanarchy,relativegains, and cooperationbasedon

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AmericanPoliticalScienceReview Vol. 85these models problematic.Finally,a morecompleteunderstandingof the relationbetween the system'scon-straintsand the originsof the concern orrelativegains also shows there is nothingtheoretically special about the possibleuse of force. Ifthe natureof military ech-nology is such that one state can turn arelativegain to its advantageand the dis-advantage of others, then these con-straintswill induce a concernfor relativegains and this may impede cooperationabsent any superior authority to ensurethat these gains not be used in this way.But if, for example, the nature of anoligopolistic market is such that a firmcan use a relativegainin marketsharetoincrease ts long-runprofitsat the expenseof other firms, then this systemwill alsoinduce a concernfor relativegains thatmaymakecooperationdifficult.Thecon-cern for relative gains may characterizemany domains,anda morerefinedunder-standing of the origins of this concernhelpsto identifythem.7I will examinea very simpleneoliberalinstitutional model of the problem ofcooperation.The examination hows thatthe repeatedgamesofferpoor modelsoftheproblemof conflictandcooperationnstructural ealism.I will thenmodify themodel so that theconstraints f themodi-fiedmodel createopportunities ora stateto turn relative gains to its advantage,whichin turn,inducesa concern or rela-tive gains. I then use this modelto studyhow changes in these constraintsaffectthe feasibilityof cooperation.

A Simple NeoliberalInstitutional ModelThe essence of the neoliberal institu-tionalanalysisof theproblemof coopera-tion is that the shadowof the futuremaylead the egoistic states hypothesizedinstructural ealism o cooperate. Repeatedinteractiongives each actor the ability

to punish uncooperativebehaviortodaywith futuresanctions.Ifthe shadowof thefuture looms sufficiently large, then thefuture costs to uncooperative behaviorwill outweigh the immediategains; and,weighingcosts againstbenefits, even ego-istic stateswill cooperate.This logic is, inturn, formalized n the neoliberal nstitu-tional analysiswith a repeatedprisoner'sdilemma nwhichmutualcooperation anbe sustained as an equilibriumoutcomewith a strategy of punishing defectionshould it occur.8First, I will presenta simpleneoliberalinstitutionalmodel of theproblemof con-flict and cooperation.The model hasbeenexplicitly designedto capture he essenceof the neoliberal nstitutionalanalysisinthesimplestpossibleformalsettingand tobe as similar to a repeated prisoner'sdilemmaas possible.Thissimilarityhelpsto clarifythe relationbetweenthe formal-ization used here and that employed inotherworkon neoliberalnstitutionalism.Second,I will demonstrate hat the modelactually does capturethe essence of theneoliberal analysis problem of coop-eration. Finally, repeated games areshown to be poor models of the problemof absolute and relative gains andcooperation n structural ealism.The simple neoliberal institutionalmodel is a three-by-threegame that isplayedtwice. The states, in keepingwithneoliberal institutionalism,will try tomaximizethe absolute sum of theirfirst-and second-periodpayoffs. The secondplay of the game casts a shadow of thefutureonto the firstplay of thegame.Butbecause the game is only played twice,thereis no shadowof the futureto affecttheprospectsof cooperationnthesecondperiod. Thus,theproblemof cooperationreduces to seeing if the shadow of thefuture makescooperationpossiblein thefirst period. In this way, the two-periodrepeatedgame providesa formalsettingfor studyingthe problemof conflictandcooperationthat is simplerthan the in-

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International Relations Theory

finitely repeatedprisoner'sdilemma.9The three-by-threeame, whichwill beplayed twice, will be called 'and s de-rivedfromthe prisoner's ilemmaby add-ing a third strategy to the two-by-twoprisoner'sdilemma.Thereare two states,Si andS2, in thisgame;and each hasthreestrategies:F, T, and C. Figure1 showsthepayoffs to the variouspossibleoutcomes.The four cellsat the upper eftforma sim-ple prisoner's ilemma n whicheach statestrictlyprefersplayingTto Fregardless fwhetherthe otherstate is playing T or F.But if both states play T, they areworseoff than if both had played F. The out-come (T, T)is Pareto-inferioro (F,F). Ifone state playsC, thenthat state'spayoffsare zeroregardless f what theother statedoes-while the other state obtains 0,-1/2, or -1 if it plays C, T, or F,respectively.It is importantto emphasizethat thegame composedof two plays of 6is anextreme theoreticalsimplification.6hasbeenexplicitlydesigned o thatit capturesthe essence of an infinitely repeatedprisoner's dilemma and the neoliberalinstitutionalanalysis of the problem ofcooperation n the simpler ormal settingof a two-period repeatedgame. At thislevel of abstraction, serves as a substan-tive modelof the international ystemorof the international conomyonly in thevery general ways that the repeatedprisoner's dilemma does in neoliberalinstitutionalor structural ealistanalysesof the problemof cooperation.Neverthe-less, 6'may be given a more concreteinterpretationhat is roughlybasedon anoptimaltariffmodel, and describing hisinterpretationmay help to make theanalysis clearer. Building on Johnson's(1953) seminal work on optimal tariffs,thestrategiesF, T, C may denotefree andopen trading policies, impositionof theoptimal ariff, andclosureof the economyby trade prohibition, respectively. Byassumption, there are only two states;

Figure1. A NeoliberalInstitutionalModelS2

F T C

F 3,3 1,4 -1,0

S1 T 4,1 2,2 -1/2,0

C 0,-1 0,-1/2 0,0

consequently,the option of closing theeconomy is equivalent to imposing anembargo.10 he game 4' then, representsthe case in which a stategains if it is theonly state to impose a tariff but bothstates ose if theyboth imposetariffs; hatis, the outcome in which both statesimpose tariffs (T, T) leaves both statesworse off than the free trade outcome,(F,F). Ifboth states closetheireconomiesand effectively embargo each other byplaying C, there will be no trade. Thepayoffs in this case are less than the pay-offs obtainedif both states had imposedan optimal tariff.1 If only one of thestates closes its economy, there will stillbe no traderegardlessof what the otherstate does; and the state that closed itseconomyreceives hesamepayoff regard-less of what the other state does. But thestate that had expected to trade, eitherfreely or with tariffs, suffersa loss dueto a misallocation of its productiveresources.Accordingly,each state prefersto close its economyif the otherdoes. For

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AmericanPoliticalScienceReview Vol. 85the sake of clarification, heneoliberaln-stitutionalmodelcomposedof playing 4'maybe loosely interpreted s a veryrudi-mentarymodel of strategic rade. 2The formal aspects of the neoliberalinstitutional critique of structuralreal-ism'sanalysis of the problemof coopera-tion are based on a repeated prisoner'sdilemma in which the shadow of thefutureis large enoughto inducecoopera-tion. Inorderto relatethe present ormal-izationto thatemployed n theneoliberalinstitutional critique, the payoffs of themodel developed here have been con-structedso that the shadow of the futuredoes induce cooperationin the model.More formally, the neoliberal institu-tional model has beenexplicitly designedso that (F, F) is a first-period quilibriumoutcome. 3To show that(F,F)can be a first-periodequilibrium utcome,theequilibriaof theneoliberal institutional model will bedetermined.In equilibrium, he outcomeon the last play of a repeatedgamemustbe an equilibriumof the stage game thatis being repeated.14 In particular, thesecond-period utcome of the gamecom-posed of two plays of the stage game 4'must be an equilibriumof 4' 4g in turn,has two pure-strategy quilibria.15n thefirst equilibrium,each state imposestheoptimaltariffand receivesa payoff of 2.In the secondequilibrium, achstateem-bargostheotherby closing tseconomytotrade. Thisyieldsthepayoffs(0,0 ). Thus,in the game in which 6is played twice,theonly second-period utcomesthatcanbe part of an equilibriumare (T, T) and(C, C).16Playing 4'twice does, however, affectthe first-period utcomes that canbe sus-tained in equilibrium.Indeed, the freetradeoutcome (F, F) as well as the out-comesin whichone stateimposesa tariff,(T. F) and (F, T), can occur in equilib-rium.Forexample, heequilibriumtrate-gies that lead to (F, X in the firstperiodarefor S1to play F in the firstperiodand

Tin the secondperiod f (F,F)is thefirst-period outcomeand C if not and, similar-ly, forS2 o playFin thefirstperiodandTin the second periodif (F, F)is the first-period outcomeand C if not. In essence,the state that remained faithful to freetrade duringthe first period by playingFis punishing the defector in the secondperiod by imposingan embargo.Clearly,(F, F) is the first-periodoutcome if bothstatesfollow thesestrategies.Thesestrate-gies also constitute an equilibrium ifneither state can improve its payoff bydeviatingfromits strategy,given thattheother player is following its strategy. Ifboth states follow these strategies,eachreceives threein the first period and twoin the second for a total payoff of five. If,however, a state deviates in the firstperiod by playing T, it will do betterinthat period by realizinga payoff of four.But given the other state's strategy ofimposinganembargon the secondperiodby playing C if (F, F) was not the first-period outcome, the most that a defectorcan attain is a second-periodpayoff ofzero. This yields a total payoff of four;thatis, thefuturecostof defection,whichis to obtain zero rather than two in thesecond period, outweighsthe immediategain to defecting, which is four ratherthan three in the first period. No playerhas any incentive to deviate from thestrategiesjust described,so these strate-giesconstituteanequilibriumwhose first-periodoutcomeis (F, F).17 Thus, threatsto punishcan be used to sustaincoopera-tion in this model. Similarstrategieswillalso support (F, T)and (T F)as equilib-rium outcomes. 8As in the neoliberal institutional cri-tique of structural ealism, anarchydoesnot imply a lack of cooperation. Theequilibriaof this model are consistentwith thelackof a commongovernment nthe sensethat they aresubgameperfect. 9This means that carryingout the threat-enedpunishment f imposinganembargoin equilibriums in the threatener's wn

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International Relations Theoryself-interest.Neitherstatecanimprove tspayoff by backingdown and not follow-ing throughon its threat,given the otherstate's strategy.20Because implementingthe threat to punish deviation is in thethreatening tate'sown interest,the equi-libria supporting (F, F),(T, f, or (F, T)donot implicitlyrequirethat some externalauthority exists to enforce threats orpromisesthat are in a state's interesttomake but not necessarilyto implementshould the time come to do so. In thissense,these equilibriaarein keepingwiththenotionof international narchyas theabsenceof a central authority.Coopera-tion, even in anarchy,is possible.2"Insum,the repeatedprisoner's ilemmahas been widely used to providethe for-mal underpinnings f the neoliberal nsti-tutionalanalysisof the problemof inter-national conflict and cooperation. Therepeatedgamecomposedof twice playing4'formalizesmuch of the essenceof theneoliberalinstitutionalcritiqueof struc-tural realism in a simpler setting. Theshadow of the futuremakescooperationpossible even in an anarchicsystem inwhich each state judges "its grievancesand ambitionsaccordingto the dictatesof its own reason" (Waltz 1959, 157)because there is no authority that issuperiorto the states. In particular,thecooperativeoutcomein whichboth statesmaintain open economies and receiveequal absolutegains can be supported nequilibrium.Thisequilibriumofferseachstate a payoff of five in the repeatedgame. The absolute gains are equal, sothere are no relative losses. There are,however, also equilibriumoutcomes inwhich the states' absolutegains are un-equaland, therefore,one of thestatessuf-fers a relative loss. For example, in theequilibriumn which(F, T)is the outcomein the firstperiod,S1 receivesfour in thefirst period and two in the second for atotal of six. S2 receives one in the firstperiodand two in thesecondfor a total ofthree. Because these are equilibrium

payoffs, the statesufferinga relative oss,whilecertainlypreferring higherpayoff,cannot improveits payoff by altering tsstrategy.Inthis sense, this state is uncon-cernedby its relative oss.Althoughtherepeatedprisoner's ilem-ma provides the formal foundationsforthe neoliberal institutional critique ofstructural ealism'spessimisticassessmentof the prospectsfor cooperation n anar-chic systems, repeated games, includingthe repeatedprisoner'sdilemmaand thesimple neoliberal institutional modeldevelopedhere, formalizestructural eal-ism's understandingof the internationalsystemand, especially he role of forceinthat systemverybadly. This, in turn,sig-nificantly weakens any analysis of theproblemof relativegainsand thefeasibili-ty of cooperationbased on this type offormalization.Repeatedgames are poormodelsfor two reasons.The first is more readilyapparentbutless directly related to the problem ofabsoluteandrelativegainsandtheeffectsof the concernfor relative gains on theproblemof cooperation.Structural eal-ism, as well as realism,22ocuseson a sys-tem in which states have the option ofusingforce if that seems to them to be intheir best interestand in which the useof force may transform he system. ForAron, international elations"present neoriginalfeaturewhichdistinguisheshemfrom all other socialrelations:they takeplace within the shadow of war"(Aron1966, 6). ForWaltz,force in internationalrelations"serves,not only as the ultimaratio, but indeedas the first andconstantone. . . . The constant possibility thatforce will be used limits manipulations,moderates demands, and serves as anincentivefor the settlementof disputes"(1979, 113). And for Gilpin, hegemonicwar is a principle means of systemicchange (1981,42-49).Giventhe centralrole that the possibleuse of forceplays in structural ealism, twould seem that any modelof the inter-

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AmericanPoliticalScienceReview Vol. 85national system envisionedin structuralrealismwould have to satisfytwo require-ments:(1) the optionof usingforce shouldbe representedn the model; and (2) themodel should allow for the possibilitythatthe use of force might,whether nten-tionally or not, change the system.Forarepeated-gamemodel, the first require-ment means thatone of the optionsin thestage gamethat is being repeatedshouldcorrespond o the option of using force.If, for example, the system is being for-malizedwith a repeatedprisoner'sdilem-ma, thendefecting houldbe takento rep-resentthe option of attacking. Repeatedgamescan satisfythis requirement.But repeatedgames cannot satisfy thesecond requirement, and this rendersthem poor models of the internationalsystem mplicit n structural ealism.Iftheinternational system is modeled as arepeated game, then the state of thesystem(i.e., the actors,the optionsavail-able to the actorsin eachperiod, andthepayoffs to the variouspossiblecombina-tions of actions)remainsconstant.Everyperiodlooks like every otherperiodin arepeatedgame. Nothingtheactors do canchangethe stateof the system.Fightingahegemonicwar in one period does notaffect the constraints acingthe actorsinthe next period. If, for example, bothstates defect in any round of a repeatedprisoner'sdilemmaand this is interpretedas fightinga hegemonicwar, then a hege-monic war can never changethe system;for immediatelyafter the war, the samestates simplyplay the prisoner'sdilemmaagain and the game continues on as ifnothinghad happened.Put anotherway,using a repeatedgameto model the inter-nationalsystemis to say that the systemin 1939 was formally equivalentto thesystem that emerged in 1945. Becauseforce can neverchangethe systemif thissystemis formalizedas a repeatedgame,formalizingthe internationalsystem in-herent n structural ealism n this way isquite problematic.

The second reason that repeatedgamesformalize structuralrealism'sconceptionof the internationalystempoorly is moresubtlebut also moredirectlyrelated o theproblem of absolute and relative gainsand the feasibility of cooperation. Theconcern or the relativegainsin structuralrealism arises because a state's relativeloss to another state may be turnedagainst it as that other state pursuesitsown ends: "If an expectedgain is to bedivided, say, in the ratio of two to one,one state may use its disproportionategain to implementa policy intended todamage or destroy the other" (Waltz1979, 105). If, therefore,a model is toprovidea good formalization f structuralrealism's conceptualizationof the prob-lem of relative and absolute gains, thereshould be some way for a state in thatmodel to use a relativegainto its advan-tage and to the detrimentof the otherstate. Unlesssuch an option exists in themodel, thereis no reasonfor a state to betroubledby a relative oss, and the modelis not capturingwhat structuralrealismsees as theessenceof theproblemof rela-tive gains and cooperation.But no suchoption exists in repeatedgames; conse-quently, they assume away what struc-turalrealism akesto be the essenceof theproblemof relativegainsandcooperation.That thereis no way for a state'srela-tive loss to be turned against it in arepeatedgame is easiest to see by con-sideringhow actorssustaincooperationnrepeatedgamesand then showing that astate's abilityto induce the otherstate tocooperate is unaffectedby any relativelosses.To sustaincooperationn anytwo-actor game, each actor must be able tomake the long-runcosts of defectionforthe other actor outweigh the immediategains.Thefuturecosts thateach actorcanimposeon theother determinewhetherornot the actors can sustain cooperation.But in a repeatedgame, an actor'sabilityto make the future costs of defectionhigherthan the immediategain does not

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InternationalRelationsTheorydependonhow well that actorhas doneinthepast relativeto thepotentialdefector.If, for example, a sanction must beimposed for five periods in a repeatedgame to make the cost of defectionexceedthe gain, then it will always take fiveperiodsto do this regardlessof how wellthe actorshave done in relation to eachother before the sanction is imposed.Because he abilityto imposefuturecostsdoes not dependon how well the stateshave done relativeto each other, achiev-ing a relative gain or sufferinga relativeloss does not affect a state's ability toinducecooperationwith threatsof futurepunishment.A state that has suffered aseries of relative losses can threatentoimposejustasmuchfuturepunishment nthe otherstateas it wouldhave been ableto threatenhad it not suffered heserela-tive losses. Relative osses do not impedea state'sabilityto enforcecooperationn arepeatedgame. There is, therefore, noreasonto be concernedwithrelativegainsor losses. Thus, the formalism of arepeatedgameomits whatstructural eal-ism sees as the very essenceof the prob-lemof absoluteand relativegains.For hisreason, repeated games formalize theinternational ystemimplicit n structuralrealismvery badly.23A more satisfyinganalysisof the prob-lem of relativegainsand the feasibilityofcooperationrequiresa modelin whichtheoption of using force is representedexplicitlyand in which a state's relativeloss may be turnedagainstit. Using theneoliberal institutional model analyzedhere as a point of departure, I nextdevelop a model that satisfiesthese tworequirements. n that model, each state'sabilityto use force successfully o achieveits ends will dependon how well it haspreviously done relative to the otherstate.

A StructuralModel of theProblemof Absoluteand RelativeGainsI developa very simpleand highlystyl-izedformalization f theproblemof abso-lute and relative gains. States will nowhave the explicitoption of using force ifthat seems to them to be in their bestinterest.More mportantly, hemodel hasbeen explicitly designedso that relativegains and losses matter because they

affecta state'sabilityto use forcesuccess-fully to furtherits interests.As will beseen, theseconstraintsactuallydo inducea concern for relative gains. For thisreason,thismodeloffersa betterformali-zation of the structuralrealism'sunder-standingof the problemof absoluteandrelative gains.Because the constraints in the modelformally induce a concern for relativegains, the modelmay be used to examinehow changes in these constraintsaffectthe states' relative concern for absoluteand relative gains and the feasibilityofcooperation.This examination hows thatmany important aspects of neoliberalinstitutionalism and structural realismemergeasspecialcasesof themodel.Iftheuse of forceis at issuebecausethe cost offighting is sufficientlylow, cooperationcollapses n the model. Thisis in keepingwith the expectationsof structuralreal-ism. Butif the use of forceis no longeratissue,cooperationagainbecomes easible.This is more in accord with neoliberalinstitutionalism.The model thus offersasynthesis of the apparently conflictingperspectivesof neoliberal nstitutionalismandstructural ealismon theproblem orrelativegains and the feasibilityof coop-erationby explainingvariations n therel-ative concernof relativegainsand in thecorresponding easibility of cooperationin termsof changes n the constraints ac-ing the states and not in terms of theattributesof the states.The model also addressestwo other

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American Political Science Review Vol. 85

Figure2. The Option of Fighting

A ANA NA

S1 S2

issues in internationalrelations theory.First, the structureof the internationalsystem as Waltz definesit will be shownto remainconstantthroughout he analy-sis. Yet the feasibility of cooperationvaries.ThismeansthatWaltz'snotion ofstructure s unable to account for thesechanges n the feasibilityof cooperation.Second, the model clarifiesthe relationbetween anarchy and cooperation byhelping to explainwhy anarchydoes notimply a lack of cooperation n some sys-tems but does impede cooperation inothers as neoliberalinstitutionalismhasshown.The specterof war is introduced ntothe model by assumingthat each statemust decide whether or not to attackbetweenthe two playsof 6As illustratedin Figure2, after the first play of & S1chooses between attacking, A, or notattacking,NA. If S1attacks,there s war.If S1does not attack, thenS2mustdecidebetween attackingor not. If S2 attacks,there will also be war. If S2 does notattack,thenthere s no warandthegameends with the secondplay of &To complete the specification of themodifiedgame, the payoffs to attackingmust be defined. This specificationdepends, n turn,on makinga fundamen-tal assumptionabout the natureor tech-nology of warfare;and it is at this pointthatrelativegainsformallyenter he anal-ysis. The very simple, highly stylizedassumptionabout the nature of warfare

underlying this analysis is that thestrongera stateis economically, hemorelikely it is to prevail n war. Thus,relativegains matterbecausethey affect how thestates are likely to fare in theevent of warand thus affectthe states'futureexpectedpayoff.Itis important o emphasize,how-ever, that relativegainsaresignificantnotbecause a state's utility is a function ofthem-the states are still trying to max-imize their absolute gains-but becausetheconstraintsmposedby theunderlyingtechnology of warmakes it possiblefor astateto use its relativegains to its advan-tage and to the disadvantageof the otherstate.24To formalize a stylized technology ofwarfare n which relativegains and lossesaffect a state's ability to prevail in theevent of war,thepayoffs to attackingwillbe takento dependon whathappenedonthefirstplay of 4'The statesare assumedto be roughly equal before the gamebegins, so that the states will fight to astalemate f there is war and if the differ-ence between the first-periodpayoffs istoo small to give one state a significantmilitaryadvantage.More specifically,ifone state attacks and the differencebe-tween the first-periodpayoffs is less than3, then both states will fight to a draw,paying a fighting cost of 3.5, and thenplay 6'for a second time. Thesepayoffsare shown in Figure3, where 6'- t3.51 sthepayoffmatrixobtainedby subtracting3.5 from eachpayoff in 6If thedifferencebetweenthefirst-period ayoffsis at least3, then the state with the higher payoffwill be assumedto be sufficientlystrongeconomically hat it will prevail f there swar. If a stateprevails,thenits payoff tothe entiregameis what it receivedon thefirst play of 4, which must have been 4(for otherwise the differencebetweenitspayoff andthe otherstate'spayoff wouldhave been less than 3) less the cost offighting, 3.5, plus the payoff to victory,which will be takento be 6. In sum, thetotal payoff to prevailingis 6.5. Defeat

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InternationalRelationsTheoryFigure 3. The PayoffsIf Fighting Brings Stalemate

? - (3.5) - (3.5)

A A

E : NA NA ?S. S2

meansa loss of 3.5 dueto the cost of fight-ing plus0, whichwill be takenas the pay-off to defeat. Thus, the total payoff if astate is defeated s the first-period ayoff,whichmusthave been 1 if the differencebetween the states' first-periodpayoffswas at least 3, less the cost of fighting,3.5, for a net of -2.5. These payoffs aredepicted n Figure4.The prospectof war renderscoopera-tion in the first play of impossible.Clearly,theoutcome(T,F)cannotbe sus-tained as a first-periodequilibriumout-come. If Si imposesa tariff and S2main-tainsan openeconomy,thenSi is sure toattack and defeat S2 because this maxi-mizes Si's payoff. The game would endwith payoffs (6.5, -2.5). S2, however,can do better han thisby playingTin thefirst period.This will give S2a firstperiodpayoff of 2; and, because war wouldmean stalemate,neitherstate will attack.S2 will therefore end the game with atleast two. Thus, S2 has an incentive todeviatefromF in the firstperiod n orderto depriveSI of its relativegain;andthismeans that (T, F) cannot be part of anequilibrium.A similar argumentshowsthat (F, T) cannot be an equilibriumoutcome.The effects of the specterof waron theoutcome in which both states maintainopen economies (F, F) illustratea pointthat suggests cooperationmay even be

Figure4. The PayoffsifS1Will Prevail(6.5, -2.5) (6.5, 2.5)

A A? / NA NA *

S S2

more difficult than has been previouslyappreciated.Because (F, F) offers bothstates equal absolute gains and conse-quently no relativegains, it might seemthat it would be possible to sustainthisoutcome in equilibrium.This, however,is not the case. Although this outcomeoffersno relativegain, deviatingfrom itdoes;and thismeansthat it cannot be anequilibrium utcome.If one stateplaysFand the other cheats with T, then the lat-ter will securea large relativegain andthen attackandprevail.Eachstate,there-fore, has an incentive o deviate fromFiftheotherplayer s playingF, so (F, F)can-not be an equilibrium utcome.Anarchyand the possible use of force may evenprevent he realizationof agreementshatprovide equal absolutegains if deviatingfrom the agreementwould yield largerelativegains.These results are in keepingwith theexpectations of structural realism.Althougheachstatein the modelis tryingto maximize tsabsolute evel of economicwelfare, t is doingso withinananarchicalstructurewhoseunderlying echnologyofwarfaremeans that the relativegains ofanothercan be turnedagainstit so as toreduce its future level of economic wel-fare. These constraints orce the states tobe concernedabout relativegains in thesense that outcomes that offer unequalabsolutegainsor the prospectof unequal

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American Political Science Review Vol. 85

absolutegains should one state cheat onan agreement annotbe sustained n equi-librium.The only first-period quilibriumoutcomes n the model arethose in whichboth states imposetariffs(T, 7) or closetheireconomies (C, C).But if the constraints acing the stateschange, the conclusions are more in ac-cord with the expectationsof neoliberalinstitutionalism.In particular, coopera-tion reemerges nce the use of force is notat issue. To formalizethis, supposethatthe cost of fightingrises from 3.5 to 7.Thenthe payoffto victory is 4-7 + 6 =-1, to defeat, 1 -7 + 0 = -6. In thesecircumstances,a state prefers not to at-tack even if it has secureda relativegainon the first play of 4 Even f sure of pre-vailing, no state will resort to force;andcooperationagain becomesfeasible n themodel.To sustain(F,F), for example,thestate'sequilibrium trategieswould be toplay F in the first play of 6 not attack,and then play T in the second period ifbothstatesplayedFin the firstperiod.Ifastatedeviated romFin thefirstperiodorif a state attackedand the war ended in astalemate,then the states would sanctioneach other duringthe second period byplaying C. To see that these are, in fact,equilibriumstrategies that do support(F,F) in the firstperiod,note that if bothstatesfollow them,theneach receives3 inthe first period,does not attack,and thenobtains2 in the secondperiodfor a totalof 5. If S1deviatesfromFby playing T, itwill receive4 in the firstroundand thenmust decide whetheror not to go to war.If it does, it will prevail,but its totalpay-off will be the first-period ayoffof 4, lessthe cost of war, 7, plus the payoff to vic-tory, 6. The overallpayoffof deviating nthis way is 3. This, however, is less thanSi would have obtained had it followedtheoriginalstrategy.Si, therefore,hasnoincentive o deviateby playingTand thenattacking.Si also has no incentive o devi-ate by playing T in the first period andthen not attacking,for S2will be playing

C in the second period because of Si'sdeviationfromF. In thiscase, S1'spayoffwill be 4 + 0 = 4. Si, therefore,has noincentive to deviate from the strategyspecified;nor, by a symmetricargument,has S2. These strategies husconstituteanequilibrium hat leads to the cooperativefirst-period quilibrium utcomes.In brief, cooperationcollapses in themodel when the use of force is at issue.Thisis in keepingwith structural ealism.But if the cost of war is sufficientlyhighthat the use of forceis no longerat issue,thencooperationagainbecomespossible;and this is in accordwithneoliberal nsti-tutionalism. Thus, the simple modeldevelopedhere integratesmuch of struc-turalrealismand neoliberal nstitutional-ism within a common analytic frame-work, in that many aspectsof these twoapproachesappearas specialcasesof thepresentmodel.The structuralmodel illuminatestwoother issues in international relationstheory. First, it formally shows thatWaltz's notion of a political structure(1979, 79-101) cannot explainthe varia-tion in the feasibilityof cooperationcon-sideredhere. The political structure,asWaltz defines it, remains constant andunchanged hroughout he analysis.Con-sequently, structural changes as Waltzconceivesof themcannotaccountfor thevariations in the likelihood of coopera-tion. Explaininghe rangeof cooperativebehaviorexaminedhere requiresa moredetailedexaminationof the system'scon-straintsthan Waltz's definitionof struc-turepermits.To seethatthe threecharacteristicshatdefinea politicalstructureor Waltz,i.e.,the distributionof capabilities,the func-tional differentiationor nondifferentia-tion of the units, and the orderingprin-ciple,remainconstant,notethatthegameis completelysymmetric.There are onlytwo states, and the only differencebe-tween them is that one is labeledSi andtheother s labeledS2.Thus,as thecost of

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InternationalRelationsTheoryfightingvaries, there is no change in thedistributionof capabilitiesor in the func-tional differentiationof the states. Theorderingprinciple also remains that ofanarchy, in that the games are alwaysanalyzed in terms of subgame perfectequilibria.The political structure,there-fore, remains onstant,although hefeasi-bility of cooperationvaries.The second issue in international ela-tions theory is the relationbetween anar-chy and cooperation. Cooperationcol-lapses when the use of force is at issue.But anarchy in the sense of a "lack ofcommon government" o enforce agree-ments is not in and of itself the cause ofthis collapse.No such authorityexists inthe neoliberal institutional model inwhich 6'was simplyrepeated wice or inthe structuralmodel. Yet, cooperationwas anequilibrium utcome n theformerandin thelatterwhenthe use of forcewassufficiently ostly. Anarchy,as neoliberalinstitutionalism rgues,does not logicallyimply a lack of cooperation (Keohane1984, 65-84).Whataccountsfor the lackof coopera-tion is not anarchyfor this is present inall of themodels.Rather, he explanationlies in thedifferent ets of constraints hatdefinewhat the statescan do in anarchy.In the structuralmodel when the use offorce s at issue,as it is in theinternationalsystem envisioned in structuralrealism,relative gains matter. In these circum-stances, the constraints n the structuralmodelformallycreatean opportunity oreachstateto exploit its relativegain to itsown advantageand to the detrimentofthe otherstate. Suchconstraintswill theninduce a concernfor relativegains unlessthere s a centralauthority hatcanensurethatno statewill exploit the opportunityaffordedby these constraints.Coopera-tion, therefore,collapses or two reasons.Theconstraints reateopportunitiesor astate to exploit its relative gains to itsadvantageandto the disadvantageof theother state; and there is no common

governmentto ensurethat states do notexploit these opportunities. In contrastwith the structuralmodel, anarchydoesnot imply a lack of cooperation in theneoliberal institutional model, becauserelativegains do not matter n thatmodel.As I have shown, each state'sability todeter defectionwith the threat of futurepunishmentdoesnot dependon how wellthatstate has donerelative o the other na repeatedgame. The constraints n theneoliberalnstitutionalmodel do not offerthe statesa way to exploita relativegain.Consequently, here s no need for a com-mon government o ensurethat the statesdo not exploit opportunitiesto turn arelativegain to theiradvantage,becausethere are no such opportunitiesin themodel.In sum, two factorscombineto inducea concern for relative gains and makecooperation difficult. The first factor,whichheretoforehasonly beenimplicit nstructural realism's description of theinternational system, is that the con-straintsdefining he systemcreateoppor-tunities or one stateto turnrelativegainsto its advantageand to the disadvantageof other states. The second factor, onwhich both structuralrealist and neo-liberalinstitutionalanalysesof the prob-lem of relative gains and cooperationhave focused, is anarchy.25f opportuni-tiesto exploit relativegainsexist, thentheabsence of a commongovernment o en-sure that the states do not exploit theseopportunitiesmay impedecooperation.By emphasizing hat structural ealismimplicitlyassumes hatthenatureof mili-tary conflict meansthat the potential useof force creates a set of constraintsinwhich states can exploit their relativegains, I may have obscureda more gen-eralpoint. Thegeneralproblemconfront-ing a state in this system is one of con-strainedoptimization n which the unitsaretryingto maximize heirabsolute evelof economic welfare subjectto a set ofconstraints n which a unit'scurrentrela-

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AmericanPoliticalScienceReview Vol. 85tive gain may be translated nto a futureabsolute gain for that unit and a futureabsolute loss for the other units. If thismore general descriptionalso applies toother systems, then the present analysismay also help to explainwhy cooperationmay be difficult to achieve in those sys-tems even though the units in those sys-tems are attempting to maximize theirabsolute gains and the possible use ofmilitary orce is not a relevantpart of theproblem. If, for example, long-runprofitmaximizationwithin an oligopolisticmar-ket structuredependson relativegains interms of, say, market share, then thisanalysiswould suggest hat it may be verydifficult o achieve international oopera-tion and collaboration even if nationalsecurity concerns are not at issue.26Describing the problem faced by statesin the international ystem in the moreabstractterms of the optimizationprob-lem confrontingthem may suggest pre-viously unappreciatedparallels betweenthis and other problemswhere the possi-ble use of force is not the source of theconcern or relative gains.

ConclusionsThe problemof absolute and relativegains divides neoliberal institutionalism

and structural realism. The formerassumes that states are primarilycon-cernedwith absolutegainswhile thelatterassumes that states are primarilycon-cerned with relative gains. What toassumeaboutstates'preferencess a theo-retical question, not an empiricalone.States as rational unitaryactors do notexist. They are a theoretical construct.Thus, the questionof whetherstatesmax-imize absolute gains or are concernedabout relativegains is empiricallymean-ingless. The real question is, Whichassumption about state preferences ismore useful?Which in the context of abroader theory gives rise to better

insights?Any firm judgment about thismust await furtherwork. As a first steptoward this judgment, I have begun todescribesome of the insightsthat followfromexamininga simplemodel in whichstates are assumed to be attempting tomaximize heirabsolute evel of economicwelfare in an anarchic nternational ys-tem in whichan absolutegain but relativeloss today can become an absolute losstomorrow.This simplemodel takes a step towardbringing neoliberal institutionalismandstructural ealismwithin a single analyticframeworkby showingthat manyaspectsof these two approachescan be seen asspecialcases of the model. In keepingwiththe expectations of structural realism,states are concernedabout relative gainswhenthe possibleuse of forceis at issue.Cooperativeoutcomes that offerunequalabsolutegainscannotbean equilibriumnthis system. Indeed, even some agree-mentsthatoffer equal absolutegains,andtherefore,no relativegain cannotbe sus-tained in equilibrium,because one statecan achieve a relativegain by defectingfrom the agreement. The prospects forcooperationare, however, sensitive o thecosts of fighting.If the use of forceis nolongerat issue, then a state'srelative osswill not be turnedagainst hatstate.Rela-tive gainsno longer matter,andcoopera-tion now becomes feasible. This is inkeeping with the expectations of neo-liberal institutionalism.The modelalso furthers he analysis oftwo otherissuesin international elationstheory. First,it providesa simpleformalexampleshowingthat Waltz'scharacteri-zation of a system'spoliticalstructure nterms of its orderingprinciple,the func-tional differentiation f its units, and thedistribution f capabilities cross heunitscannot accountfor the variations in thefeasibilityof cooperationexaminedhere.Changes n the cost of war do not affectthe system'sstructure n Waltz's ormula-tion but do affectthe potentialfor coop-

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InternationalRelationsTheoryerationin the model. Second, the modelhelps to clarifytherelationbetweenanar-chy and cooperation.Anarchy, as neo-liberal institutionalismhas shown, doesnot imply a lack of cooperation.Rather,two factorscombine o makecooperationdifficult.Thefirst is anarchy,definedas alack of a common governmentthat canenforcecommitments.The secondfactor(crucial to structuralrealism but onlyimplicit n it) is that thesystem be charac-terizedby a setof constraints hatpresentthe states with opportunities in whichtheycanuserelativegains to theiradvan-tage and to the disadvantageof others.Absentsuch opportunities,relativegainscannot be exploited,and there s no needfor a central authority to ensure thatthese nonexistent opportunitiesare notexploited.

NotesI thank David Collier, MichaelDesch, JamesFearon, Jeff Frieden, Avery Goldstein, JoanneGowa,JosephGrieco,Keisuke ida,EthanKapstein,RobertKeohane,JamesMorrow,RonaldMitchell,KamalShehadi,R. HarrisonWagner,and CelesteWallanderor helpfulcommentsandcriticisms.1. Fordiscussions f neoliberalnstitutionalism'semphasison absolutegains and realism'sor struc-turalrealism's mphasison relativegains, seeGilpin1981, 18-25; Gowa 1986, 172-79; Grieco 1988a,1988b, 1990; Hoffmann1973, 6-12; Jervis1988,334-36; Keohane1984; Keohaneand Nye 1977,23-37; Keohaneand Nye 1987, 728-33; Krasner1983, 356; Lipson1984, 12-18; Mearsheimer990,11, 44-45; Morgenthau1967; Rosecrance1981,705-7; Rosecrance 986, 44-63; Snidal1981, 3-6;Stein 1983, 134; Stein 1984, 383-86; Viner 1948,1-29; Waltz 1959, 34-36, 196-98, 219-21; Waltz1979,102-28;andWolfers1962,67-115.2. Discussions f absoluteandrelativegainsandthe problem of cooperationinclude Gowa 1986;Grieco1988a,1988b,1990;Lipson1984;andSnidal1991.3. Forspecificexamplescharacterizinghe con-cernaboutrelativegains n termsof preferences,eeGilpin1981,18-21; Grieco1988a,1988b,1990;Jer-vis 1988, 335; Keohane1984, 66; Lipson1984, 15;Mearsheimer990,11,44-45;Snidal1991;andStein1983,134;Stein1984,382.Keohane lsoclaims hatmany aspectsof neoliberal nstitutionalisman be

basedon the sameset of assumptions boutstates'preferences hat structural ealismemploys (1984,67). However, Gowa (1986)in generaland Grieco(1988a) in particular argue that the repeatedprisoner's ilemma nwhichKeohanebasesmuchofhis analysis (1984, 65-84) is not consistentwithstructural ealism.4. Forotherattempts o integrateheanalysisofconflict and cooperation, see Lipson 1984, Oye1986,and Stein1984.5. Explainingtates'concern orrelativegains nterms of constraints ather hanpreferencess inci-dentallymore nkeepingwith theoriginalnotionsofstructuralrealism.Indeed,what makes structuralrealismstructural nd distinguishestructural eal-ism from realismis that the concernfor relativegains is induced by the system'sstructuralcon-straints Waltz1959,34-36).6. See Powell (1991) for an effort in thisdirection.7. ForWaltz,theconcern or relativegainsalsoextendsbeyond the international ystem to otherself-helpsystems (1979, 91). But it is difficulttodefineself-helpprecisely.8. For examplesusing the repeatedprisoner'sdilemma o formalizeheproblem f cooperationeeAxelrod1984, Keohane1984,andOye 1986.9. As is wellknown,if theprisoner's ilemmasrepeated knownfinitenumber f timesand there scompleteinformation,there is no cooperation nequilibrium.Theremust be infinitelymany repeti-tionsfor thereto be cooperationn equilibrium.f,therefore, neis to studytheproblem f cooperationformally in the context of a repeatedprisoner'sdilemma,one mustfocus on an infinitelyrepeatedprisoner's ilemma.Thepresentormulation ermitsthe formalstudyof cooperation n the simpler et-tingof a two-period epeatedgame.10. One of theweaknesses f this nterpretationsthatthestates n 6are choosing heirpoliciessimul-

taneouslyandmustenduresignificantossesbeforethey canchangetheirpolicies n the secondperiod.A bettersubstantivemodelwouldnot entailsimul-taneous decisions or would allow the states tochange their policies before sufferingsignificantlosses.11. Johnson (1953) shows that if both statesimposeoptimaltariffs, hen,depending n theelas-ticities of demand,one or both states will suffercomparedo the freetradeoutcome.Optimal ariffscannotmakebothstatesbetteroff. (Inthisanalysis,optimal tariffs are assumedto leave both statesworseoffrelative o thefreetradeoutcomes.Conse-quently,thepayoffsto (F,F)are arger hanthoseto(T. 7) in K) He also establisheshat therewill be apositive volume of tradeeven if both stateshaveimposed an optimal tariff. This implies that thestates obtain higher payoffs even with mutualtariffs hantheywould if therewereno trade.Thus,1317



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AmericanPoliticalScienceReview Vol. 85payoffs to (T, 7) arehigherthan thepayoffsto anoutcome n whichat leastone of the statesplays C.12. Foran introduction o, and surveyof, someof the recentwork on strategictrade, see Cohen1990, Krugman 986, Richardson 990, Stegemann1989, andStem 1987.13. Recall that the problem of cooperationre-duces o what canhappen n thefirstperiodbecause'isonly played wice, which mplies hatthere snoshadow of the future n thesecond period.14. If the equilibrium f a repeated ame did notrequire he states o playanequilibrium f the stagegame n the last period,then one of thestateswouldhave an incentive to deviate from the purportedequilibrium trategy n the lastperiodof the game.This impliesthat the purported quilibrium trate-gies cannot actually be equilibrium strategiesbecauseno actorcan ever have any positiveincen-tive to deviatefroman equilibriumtrategy.15. I will focusexclusivelyon pure-strategy qui-libriaand disregardmixedstrategies.16. The combinationof strategies T, 7) is anequilibrium f because no statehas any incentiveto deviatefromits strategy,given the otherstate'sstrategy.If SI plays T, then playingT offersS2itshighestpayoff.Conversely,fSIplaysfl, then alsooffersS2its highestpayoff. Similarly, C, C) is anequilibrium ven thoughit is Pareto-dominatedy(T, 7) becauseno statehas any incentive o deviatefromits strategy,giventheother state'sstrategy.IfSIplays C, thenplayingC offersS2 ts highestpay-off;conversely, f SIplaysC, thenCalsooffersS2 tshighestpayoff.17. Thereason hatcooperation an arise n equi-librium n thegame composedof a finitenumberofrepetitions f 4but not in a finitenumberof repeti-tions of theprisoner's ilemmahas to do withaverypeculiarcharacteristic f the prisoner'sdilemma,whichis that the minmaxpayoff equalstheequilib-riumpayoff. This is true of very few othergames;and when the minmaxpayoff does not equal theequilibriumpayoff, cooperativeoutcomes,as wellas any otherindividually ationaloutcome,can besupportedn equilibriumn a finitelyrepeated ameif the numberof repetitionss sufficientlyargeandthe actors do not discount the future too much.Indeed, he technical eason or adding hestrategyC to theprisoner's ilemmaormedby thestrategiesFand Tis to make heminmaxpayoff unequal o theequilibrium ayoff.Thismakes t possible o sustaincooperation n the firstperiodand thus to capturethe essence of the infinitely repeated prisoner'sdilemma n a simpler etting.Forfurtherdiscussionof the equilibria f repeatedgames,see BenoitandKrishna1985, Fudenbergand Maskin 1986, andKrepset al. 1982.18. Theproblemof multiple quilibriarequentlyplagues repeatedgames. Indeed, almost any out-come canbesupportednequilibrium.More ormal-ly, any individually ationalpayoffscanbeapproxi-

mated n thelimit f thegame s repeated ufficientlyoftenand the actorsdo not discountthe future oomuch (Benoit and Krishna1985; FudenbergandMaskin1986).The existenceof multipleequilibria uggests hatone purposeof institutionsand regimesmay be tofocusexpectations n a particular quilibrium.Thisis certainly n keepingwith the notionthatregimesare "setsof implicit or explicitprinciples,norms,rules, and decision-makingprocedures aroundwhichactors'expectations onverge n a givenareaof international relations" (Krasner 1983, 2).Althoughsuggestive, hisis formallyratheradhoc.Ideally, one would like to formalize he institutionwithinthemodelwith theresult hatthemodelhas auniqueequilibrium.For an importanteffortalongthese linessee Morrow1990.19. SeeRasmusen 989,83-89 for a discussion fsubgameperfection.20. To see that the equilibrium upporting he(F,F) s subgameperfect, etSi'sstrategybetoplayFin the first period and T in the second period if(F, F) is thefirst-period utcomeand C if not. Simi-larly,S2's trategys toplayFin thefirstpriodand Tin the secondperiod f (F,F) is the first-period ut-come and ' if not. As shown above, neitherstatehas any incentive o deviate rom its strategy,giventhe other state's strategy, so this combinationofstrategiesconstitutesa Nash equilibrium n which(F,F) is the first-period utcome.To establish ub-gameperfection, t mustalsobe shown thatneitherstatehasany incentive o deviate romcarryingoutthe threatened mbargo,giventheotherstate's tra-tegy and that(F,F)was not thefirst-periodutcome.Suppose hatSIplayedT, rather hanF, in the firstperiod. GivenSi's strategyof playingC in the sec-ondperiod f, as is assumed, F,F)was not thefirst-periodoutcome,thenS2has no incentive o deviatefrom tsstrategyof embargoing I;that s, S2cannotimprove ts payoffby playingsomethingotherthanC, givenSi's strategyof playingC. Similarly, ivenS2's strategyof playing C in the secondperiodif(F, F) was not the first-period utcome,thenSI hasno incentive o change tsstrategyby playingsome-thing other than C, given that S2 is playing C.Neitherstate has any incentivenot to carryout itsthreat,given the other'sstrategy;and the equilib-rium s subgameperfect.21. Although heequilibria f theneoliberalnsti-tutionalmodel are subgameperfect,the desiretoconduct this analysis n the simplest ormalsettingpossiblecreatessome difficulties.These equilibriaare not renegotiation-proof Farrelland Maskin1989).Surmountinghis wouldrequiremovingto amorecomplicatedormalsetting hatwouldtend toobscurethe basic points the model is intendedtoillustrate.22. Seen. 5.23. Gowa(1986)andGrieco 1988a,1988b,1990)have alsocriticized heuse of therepeated risoner's

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InternationalRelationsTheorydilemma o modelstructural ealism'sonceptionoftheproblemof cooperation.Theircriticisms,how-ever, focus on the states' preferences and theassumptionhatstatesaretrying to maximize heirabsolutegain.24. The phrase"technologyof warfare" s usedhere becausethe nature of militarytechnologyinthisformalization onstrains he states in the inter-national ystem nmuch hesamewaythatthetech-nologyof production onstrainsirms nanoligopo-listicmarket.25. Forexamplesof thisfocus, see Oye 1986.26. Indeed,Grieco(1990)studiesthe problemofrelativegains n thecontextof negotiationsbetweenthe EuropeanCommunityand the United Statesover nontariffbarriers,a context n which it is dif-ficultto attributeany concern or relativegainstotheeffects hat a relative ossmayhaveon theprob-abilityof survival.Thisanalysishelpsexplainwhythisconcernmaynevertheless tillbepresentat leastat thelevelof firmsandwhy theymaytry to inducethegovernment o reflect heseconcerns.

ReferencesAron, Raymond. 1966. Peace and War. New York:Doubleday.Axelrod, Robert. 1984. The Evolution of Coopera-tion. New York: Basic Books.Axelrod, Robert, and Robert Keohane. 1986."Achieving Cooperation under Anarchy." InCooperation under Anarchy, ed. Kenneth Oye.Princeton: Princeton University Press.Benoit, Jean-Pierre, and Vijay Krishna. 1985."Finitely Repeated Games." Econometrica 53:905-22.Cohen, Benjamin. 1990. "The Political Economy ofInternational Trade."International Organization44:261-81.Farrell, Joseph, and Eric Maskin. 1989. "Renegotia-tion in Repeated Games." Games and EconomicBehavior 1:327-60.Fudenberg, Drew, and Eric Maskin. 1986. "TheFolk Theorem in Repeated Games with Discount-ing or with Incomplete Information." Econo-metrica 54:533-54.Gilpin, Robert. 1981. War and Change in WorldPolitics. New York: Cambridge University Press.Gowa, Joanne. 1986. "Anarchy, Egoism, and ThirdImages." International Organization 40:172-79.Grieco, Joseph. 1988a. "Anarchy and the Limits ofCooperation." International Organization 42:485-507.Grieco, Joseph. 1988b. "Realist Theory and theProblem of International Cooperation." Journalof Politics 50:600-24.Grieco, Joseph. 1990. Cooperation among Nations.Ithaca: Cornell University Press.Hoffmann, Stanley. 1973. "Choices."Foreign Policy

12:3-42.Jervis, Robert. 1978. "Cooperation under the Secur-ity Dilemma." World Politics 30:167-214.Jervis, Robert. 1988. "Realism, Game Theory, andCooperation." World Politics 40:317-49.Johnson, Harry. 1953. "Optimal Tariffs and Retalia-tion." Review of Economic Studies 21:142-53.Keohane, Robert. 1984. After Hegemony. Prince-ton: Princeton University Press.Keohane, Robert, and Joseph Nye. 1977. Power andInterdependence. Boston: Little, Brown.Keohane, Robert, and Joseph Nye. 1987. "Powerand Interdependence Revisited." InternationalOrganization 41:723-53.Krasner, Stephen. 1983. "Regimesand the Limits ofRealism." In International Regimes, ed. StephenKrasner. Ithaca: Cornell University Press.Kreps, David, Paul Milgrom, John Roberts, andRobert Wilson. 1982. "RationalCooperation in aFinitely Repeated Prisoner's Dilemma." Journalof Economic Theory 27:245-52.Krugman, Paul, ed. 1986. Strategic Trade Policyand the New International Economics. Cam-bridge: Massachusetts Institute of TechnologyPress.Lipson, Charles. 1984. "International Cooperationin Economic and Security Affairs." World Poli-tics 37:1-23.Mearsheimer, John. 1990. "Back to the Future."International Security 15:5-56.Morgenthau, Hans. 1967. Politics among Nations,4th ed. New York: Knopf, 1967.Morrow, James. 1990. "Modelling InternationalRegimes." Presented at the annual meeting of theAmerican Political Science Association, SanFrancisco.Oye, Kenneth, ed. 1986. Cooperation under Anar-chy. Princeton: Princeton University Press.Powell, Robert. 1991. "In the Pursuit of Power andPlenty." University of California, Berkeley.Typescript.Rasmusen, Eric. 1989. Games and Information.Oxford: Basil Blackwell.Richardson, J. David. 1990. "ThePolitical Economyof Strategic Trade." International Organization44:107-35.Rosecrance, Richard. 1981. "International TheoryRevisited." International Organization 35:691-713.Rosecrance, Richard. 1986. The Rise of the TradingState. New York: Basic.Snidal, Duncan. 1991. "Relative Gains and the Pat-tern of International Cooperation." AmericanPolitical Science Review 85:701-26.Stegemann, Klaus. 1989. "Policy Rivalry amongIndustrial States." International Organization43:73-100.Stein, Arthur. 1983. "Coordination and Collabora-tion." In International Regimes, ed. Stephen D.Krasner. Ithaca: Cornell University Press.

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Waltz, Kenneth.1959. Man, the State, and War.New York:ColumbiaUniversityPress.Waltz, Kenneth. 1979. Theory of InternationalPolitics. Reading,MA:Addison-Wesley.Wolfers,Arnold. 1962.Discordand Collaboration.Baltimore: ohnsHopkinsUniversityPress.

Robert Powell is Associate Professorof Political Science, University of California,Berkeley,CA 94720.

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