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 [email protected].
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
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 solutionsidentifiedby 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-RepeatedPrisoner's Dilemma," Journalof Economic Theory27 (August i982,
245-52.
For the resultsof laboratoryexperiments,see Robert Radlow, "An Experimental
Study of Cooperation in the Prisoner'sDilemma 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 iteratedPrisoners'Dilemmas 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 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 Evera's essayon
the originsof the First World War and KennethOye's chapteron
conflictduringthe 1930s. RobertJervis's
essayon theemermonetary
strucwarselucidatesinternational
genceof concertfollowingsystemic
studyof
turaldeterminants
of payoffs.
JohnConybeare'scomparative
conflict
in the 1930S, and
tradewars,KennethOye's studyof monetary
CharlesLipson'sstudyof bankers'dilemmasexaminemacroeconomic
determinants
of payoffstructure.
George Downs, David Rocke,and
of paydomesticstructural
determinants
RandolphSiversoninvestigate
offstructure
in theiressayon cooperation
in armsraces.Payoffstructure
3 See Jervis(fn. 5); 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 Prisoners'Dilemma, 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
Prisoners'Dilemma than in Stag Hunt or Chicken. To understandwhy,
consider each of these games in conjunctionwith the illustrativestories
fromwhich theyderive theirnames.
Prisoners'Dilemma: 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
(CD). If both squeal, both will draw a moderate sentence (DD). Each
prisoner'spreferenceorderingis: 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
hunter'spreferenceorderingis: 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 driver'spreference
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 borrowedRousseau's parableof thestaghuntto illustratetheinfeasibility
of realizing mutual interestsunder internationalanarchy.Rousseau used the staghuntto
illustratethe possibilityof cooperationduring his firstperiod of primativesocial interdependence. He argued thatindividualscould 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
Rousseau's 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
Prisoners'Dilemmasmayevolveintoless 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 transformed
diminishedperceivedgainsfromdefection,
somePrisoners'DilemmasintoHarmony.'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 reduceitsadversary's
fearof exploitation
(CD). Membersof allianceshave oftenresortedto
the device of deployingtroopson troubledfrontiers
to increasethe
likelihoodofcooperation.
A state'suse 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 one's gains from exploitation may have the effectof increasingone's 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 nation's commitmentto liberalism.It also
I9Williamson(fn.5).
EXPLAINING
COOPERATION
UNDER
ANARCHY
11
to prohowever,of increasingthenation'svulnerability
has theeffect,
that
example,thegovernment
tectionbyothers.In thetroops-as-hostage
an ally'sfear
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 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
country's
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.Nitze's recommendations
hinge on acceptance of the preceptsof what has come to be known as nuclear utilization
theory.Jervis'srecommendationsdepend 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
Prisoners'Dilemma 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 Prisoners'Dilemmaand 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 anotherstate'sforeigncurrency
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 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
Prisoners'Diagreementsis 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
underiteratedPrisoners'Dilemma 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,Prisoner's
Dilemma (Ann Arbor:University
of Michigan Press, i965), and subsequentessaysin Journalof ConflictResolution.
25 One commonobjectionto thisline ofargumentcenterson theirrationality
ofcooperation
if a sequence of Prisoners'Dilemmas has a known last element.On the known last play,
the immediategain fromsquealing cannot be offsetby expectationsof futurecooperation.
On the next-to-lastplay, the immediategain fromsquealing is not offsetby expectations
of futurecooperation,since bothactorsknow thatcooperationis irrationalon the last move.
And so on back toward the initialmove. This line of analysiscollapses iteratedPrisoners'
Dilemma into single-playPrisoners'Dilemma. To analystsof internationalrelations,the
importanceof this objection is limited.In internationalrelations,no experimenterdecrees
thata series of Prisoners'Dilemmas 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 driver'sdefectionin the presentmay decrease the likelihood of the
other driver's defectionin the future.27
B.
STRATEGIES
OF RECIPROCITY
AND CONDITIONS
OF PLAY
It is at this juncture that strategyenters the explanation. Although
the expectation of continuing interactionhas varying effectson the
likelihood of 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 actor's 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 Prisoners'Dilemma, see Luce and Raiffa(fn. 6), Appendix
Possible
8. Discount parameterssuch as Axelrod's"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 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 indirectexportsubanother'sviolationsof 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 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
Prisoners'Dilemma, whereactorscan reliablydistinguish
between cooperationand 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 adversary's
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 cooperationin 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 Olson's theoryof collectiveaction focuseson N-person versions
of Prisoners' Dilemma. The optimismof our earlier discussionsof cooperationunder iteratedPrisoners'Dilemma 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 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 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: 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 Snidal's 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 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.