Rethinking Realist-Neoliberal Debate: Assessing International Coordination & Equilibria, Slides of Game Theory

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Abstract

This essay examines and reformulates the realist-neoliberal debate. Focusing initially

on the issue of the attribution of goals to states, we argue that not only are goals merely

the epiphenomena of other things but also that their specification constitutes but a re-

description of strategic environments. That is, although an attribution of goals may

contribute to our characterization of outcomes, a discussion of them is not central to

the development of a theory that explains and predicts the outbreak of conflict and the

patterns of cooperation. Instead we argue that the realist-neoliberal debate should be

recast so that our central research agenda is the development of substantively specific

models that allow us to ascertain how the equilibrium to a game in which states structure

international affairs influences the types of issue-specific subgames states play, how coun-

tries coordinate to equilibria of different types, how we can characterize the coordination

problems associated with different equilibria, how states can enhance the attractiveness

of an equilibrium, and how states can signal commitments to the strategies that are part

of that equilibrium.

*This research was supported in part by a grant from the U. S. Institute of Peace. We also wish to acknowledge the helpful comments and criticism of Tom Schwartz, Peter Lange and Joseph Grieco.

Indeed, once the correct implications are identified, we can discern the components of a general theory in w h i c h the debate need not be resolved in favor of one side or the other. Instead, the debate is transformed to an assessment of the likelihood that states w i l l coordinate their actions and plans in one way rather than another, where this l i k e l i h o o d depends on a c o m p l e x nexus of things in addition to the properties of e q u i l i b r i a themselves, i n c l u d i n g subjective beliefs and chance events. E l a b o r a t i n g on these arguments, this essay recasts the issues that separate realists f r o m neoliberals so as to i l l u m i n a t e a theoretical perspective that encompasses both views and that establishes a research agenda focusing on those issues. We begin w i t h Powell's (1991) argument that goals are endogenous and dependent on circumstances. To this v i e w we add the argument that circumstances are themselves endogenous, w h i c h requires that the realist-neoliberal debate move f r o m a theoretically incomplete assessment of the consequences of particular sets of goals to the analysis of the e q u i l i b r i u m of complete systems. H o w e v e r , we go further and argue that goals are but a part of the description of outcomes and strategies rather than fundamental explanatory variables and that a continued focus on goals detracts f r o m our ability to understand international processes in any theoretically general way. Second, although metaphorical appeals to elements of game theory l i k e the repeated Prisoners' D i l e m m a and the Battle of the Sexes illustrate some fundamental relations between preference and choice, the p o s s i b i l i t y of cooperation in anarchic systems, and the problems of c o o r d i n a t i o n , those appeals have reached a point of d i m i n i s h i n g marginal returns. Such scenarios may aid in an i n i t i a l f o r m u l a t i o n , but we need to begin taking advantage of the general principles of interdependent action that game theory uncovers. We need to take note of the fact that since v i r t u a l l y every o n - g o i n g social process, however conceptualized, can be assumed to possess a m u l t i p l i c i t y of alternative e q u i l i b r i u m outcomes, opportunities to cooperate and the p r o b l e m of coordination arise nearly everywhere. C o o p e r a t i o n cannot be effective without coordination — although they are conceptually distinct (cooperation refers to the characteristics of combinations of strategies whereas coordination refers to the mechanisms whereby people are led to choose particular strategies), people cannot cooperate if they cannot also coordinate. T h i r d , the institutions and regulatory structures that service w h o l l y cooperative arrangements and those that service more competitive and conflictual world orders, are best conceptualized as mechanisms that coordinate the actions of people and of states to particular outcomes w i t h i n their respective orders. T h u s , we accept the view that regimes are either coordination mechanisms or manifestations of coordination (c.f., Y o u n g 1980, Stein 1982, Snidal 1985, K r a s n e r 1991, Garrett

1992. and that the realist-neoliberal debate is for the most part an argument about the relative attractiveness of different outcomes and about the efficacy of alternative mechanisms for coordinating to them. H o w e v e r , these institutions and structures, along w i t h the emphasis states on

relative versus absolute g a i n , as w e l l as the role of power, are themselves components of an e q u i l i b r i u m to a larger game in w h i c h states select w o r l d orders. U n t i l we m o d e l this larger game, we cannot understand f u l l y the forces that lead to the creation of these subsidiary institutions and to the derivative goals that states manifest. F o u r t h and as a consequence of our last two points, the realist-neoliberal debate ought to be recast so that the central research agenda assesses the degree of coordination required to achieve e q u i l i b r i a of different types at different levels of interaction. The argument over the type of international system that prevails is an argument about the relative ease w i t h w h i c h states can coordinate to w h o l l y non-cooperative outcomes, to partially cooperative outcomes that are characterized by c o m p e t i n g alliances, or to w h o l l y cooperative outcomes that correspond to traditional notions of collective security. W i t h i n these w o r l d orders, we should also examine how states might enhance the attractiveness of different e q u i l i b r i a , how they signal commitments to the strategies that lead to them, and, ultimately, how cooperation and c o n f l i c t across different issue areas reenforce or u n d e r m i n e the alternative w o r l d orders that characterize the interactions of states generally.

1. G o a l s and International Structures The realist-neoliberal dispute over goals is summarized by the assertion f r o m one side that "in a self-help system, considerations of security subordinate economic gain to p o l i t i c a l interest" (Waltz 1979: 107) and the somewhat more ambiguous argument from the other side that "under different systemic conditions states w i l l define their self-interest d i f f e r e n t l y... where s u r v i v a l is at stake efforts to maintain autonomy may take precedence over a l l other activities; but where the e n v i r o n m e n t is relatively benign energies w i l l also be directed to f u l f i l l i n g other goals" ( K e o h a n e 1989: 62). Of course, any such discussion should contend w i t h the legitimacy of attributing goals to collectivities and with the possibility that doing so is theoretically unjustifiable (c.f. A r r o w 1951). Nevertheless, the concept of the state as a rational unitary decision maker remains a convenient abstraction that allows us to ignore temporarily how international affairs impacts domestic p o l i t i c s and how domestic politics transforms the goals of individuals into state actions. T u r n i n g to the dispute itself, the issue of goals is largely a derivative matter. T h e central issue is the extent to w h i c h cooperation can emerge and be sustained in an anarchic e n v i r o n m e n t — in an environment in w h i c h agreements among countries to abide by particular strategies cannot be maintained by notions of collective interest or by exogenous mechanisms of enforcement. Instead, such agreements must be maintained by the i n d i v i d u a l self-interest of those w h o are party to them. In game-theoretic terms, cooperative outcomes must correspond to an e q u i l i b r i u m to the n o n -

must be endogenous to it. Indeed, we make the stronger argument that goals are an epiphenomena of the theory we seek. To see first w h y an algebraic representation of goals is u n l i k e l y to be adequate, let us accept the fact, uncontested by realists and neoliberals, that s u r v i v a l can depend on a state's a b i l i t y to form certain alliances and to preclude others. N e x t , observe that existing models of c o a l i t i o n formation reveal no simple algebraic relationship between R and alliance possibilities. Indeed, if we learn a n y t h i n g f r o m game theory, it is that ultimate payoffs need not relate to things such as power or v o t i n g weight in any simple way. F o r example, increasing a person's weight in a committee's deliberations can actually d i m i n i s h that person's l i k e l i h o o d of securing preferred outcomes to the extent that others respond to the increase with strategic counter-measures (c.f., Brams 1978, Ordeshook 1992, pp 162-4, and Schwartz 1992). It follows that whenever security plays a role in their evaluation of outcomes, actions, and strategies (policies), none of the preceding algebraic formulations can represent a l l aspects of the strategic imperatives that states confront. A n d the necessity for some p r i o r theory f o l l o w s f r o m the fact that without it we cannot ascertain what imperatives are ignored by any specific f o r m u l a t i o n. With respect to the necessity for rendering goals endogenous to some theory, we can start w i t h the supposition that states share the l o n g - r u n goal of welfare m a x i m i z a t i o n and that the theoretical dispute concerns the short term objectives of states. But whether short- or l o n g - t e r m , notice that we cannot observe goals d i r e c t l y -- we can o n l y infer them from actions and choices. A n d m a k i n g such inferences requires a substantive theory that links actions, outcomes and goals and that allows us to reject one set of postulated goals in favor of another whenever the later provides a more parsimonious interpretation of events. That is, to formulate sentences l i k e "given actions A, we infer that states are necessarily p u r s u i n g goals G," we must justify statements l i k e "A if and o n l y if G." O n l y if G uniquely implies A can we infer G from A. Thus, we cannot infer the "best" theory by arguing about goals beforehand -- the discussion of goals cannot be separated from the necessity of first formulating a theory that informs us about the meaning of actions. T h e f o r m u l a t i o n of such a theory, though, must begin w i t h the observation that "national policies both influence and are influenced by the types of w o r l d order w h i c h prevails at the time" (Wright 1965:1493). That is, the degree to w h i c h a state must concern itself w i t h relative resources depends in part on the willingness of other states to cooperate; but that willingness is itself dependent on the goals of other states, w h i c h depend on the goal and actions of the state in question, and so on. Hence, if G = G(E) denotes the dependence of the goals of states as they relate to the "environment" in w h i c h they operate the strategies of other states — and if E is itself a f u n c t i o n of G — E = E(G) — then we cannot solve separately for either G or E; instead, we must solve for both variables simultaneously.

we specify a strategic environment in w h i c h states choose ( i m p l i c i t l y or e x p l i c i t l y ) to make decisions on the basis of power - - a n environment that models anarchic systems and that renders E and G endogenous. P o w e l l (1991) avoids ad hoc formulations of goals and, by o f f e r i n g a specific mechanism that renders goals endogenous, approaches this theoretical ideal. But even his analysis is incomplete (deliberately so since his objective is merely to show how the goal of absolute gain is rationally transformed into a concern w i t h relative gain). T h e determinants of goals are the "constraints d e f i n i n g the system [that] create opportunities for one state to turn relative gains to its advantage and to the disadvantage of others" (p. 1315). In addition to technology, these constraints include the actions of t h i r d , f o u r t h , etc. parties (Powell's model is 2-person) as w e l l as the institutional structures that are set up to influence those actions. But because such constraints are clearly endogenous, Powell's analysis cannot supply any definitive resolution of the realist-neoliberal debate.

2. M u l t i p l e E q u i l i b r i a and Coordination T h e preceding discussion establishes only that goals are endogenous, whereas we also want to argue that goals are more a description of events than they are a p r i m a r y explanatory variable. Sustaining this assertion, though, requires that we attend to the task of p r o v i d i n g a theoretical structure in w h i c h that is true. In particular, we require a structure that admits of both the realist and neoliberal scenarios of c o n f l i c t and cooperation so we can ascertain the conditions under w h i c h one scenario rather than the other prevails. In this and in the next section, then, we reconsider some facts about game theory and about the concepts of cooperation and coordination that allow us to discern the general character of such a structure. F o c u s i n g in this section on game theory, we begin by noting that o w i n g to their i n i t i a l focus on s i n g l e - p l a y versions of the Prisoners' D i l e m m a , p o l i t i c a l scientists became especially concerned that the absence of effective enforcement mechanisms precluded cooperation even if cooperation is socially rational. That we can sustain cooperation as an e q u i l i b r i u m to a n o n - cooperative game by supposing that the D i l e m m a is repeated seemed l i k e the c r i t i c a l theoretical result. H o w e v e r , the evident role of regimes in coordinating society to particular outcomes has served to emphasize the relevance of a second scenario -- the 2-person Battle of the Sexes (c.f., Stein 1982, Snidal 1985, K r a s n e r 1991). R e c a l l i n g that an e q u i l i b r i u m in game theory is a vector of strategies, one for each player, such that no player has an incentive to change its strategy unilaterally, the d i s t i n g u i s h i n g feature of this game is that it has multiple e q u i l i b r i a that are not equivalent (each person prefers a different e q u i l i b r i u m ) and that are formed by non-interchangeable strategies ( c o m b i n i n g strategies f r o m different e q u i l i b r i a need not y i e l d an e q u i l i b r i u m ). That e q u i l i b r i u m

strategies are not interchangeable means that each player can choose an e q u i l i b r i u m strategy and yet an e q u i l i b r i u m outcome does not prevail. That e q u i l i b r i u m outcomes are not equivalent means that no specific outcome need stand out as an obvious point of convergence and that there is room for dispute as to w h i c h e q u i l i b r i u m outcome "ought" to prevail. T a k e n together, non-equivalence and non-interchangeability mean that the mere existence of e q u i l i b r i a need not resolve any " h e - t h i n k s - t h a t - I - t h i n k " infinite regress. T h u s , w h i l e the s i n g l e - p l a y Prisoners' D i l e m m a achieves notoriety by revealing that i n d i v i d u a l l y rational ( e q u i l i b r i u m ) choices can yield a socially "irrational" (inefficient) outcome, the Battle of the Sexes gains attention because it illustrates a circumstance in w h i c h there is no guarantee that any e q u i l i b r i u m w i l l p r e v a i l without "outside intervention" that coordinates the players choices. To this point we have not said much that is not discussed elsewhere in the literature on international c o n f l i c t and cooperation (c.f., Stein 1982, K r a s n e r 1991). H o w e v e r , we want to emphasize the theoretical basis for supposing that the things the Battle of the Sexes illustrates are pervasive. E v e n though one scenario (the Prisoners' Dilemma) so clearly illustrates the p r o b l e m of cooperation and the other (the Battle of the Sexes) illustrates the problem of c o o r d i n a t i o n , its is nevertheless incorrect to infer that cooperation and coordination are separable issues. We do not want to make the opposite error of confusing these two concepts by equating them, but any solution to the cooperation problem requires a solution to the coordination problem. Indeed, the substantive problems associated w i t h cooperation and coordination are present in v i r t u a l l y every social process. The theoretical support of this fact is p r o v i d e d , in part, by any one of the f o l k theorems of game theory (see M y e r s o n 1991 and F u d e n b u r g and T i r o l e 1992 for expository surveys), w h i c h show that the primary lesson d r a w n from the repeated Prisoners' D i l e m m a about the p o s s i b i l i t y of cooperation without exogenous enforcement does not require the d i l e m m a for its v a l i d i t y. If people give the future sufficient weight, then we can sustain any outcome as an e q u i l i b r i u m in any ongoing (repeated) social process if that outcome yields each person a payoff that exceeds his or her security value -- if it yields a p a y o f f that exceeds what each person can guarantee from unilateral (uncoordinated) action. The mechanism that supports this result is that if processes are repeated, then people have a great many strategies (even an i n f i n i t y of them), i n c l u d i n g ones in w h i c h their choices at one stage depend on choices at some earlier stage. In particular, they can punish each other for deviating from an agreement, they can punish each other for f a i l i n g to punish, and so on. E x p a n d i n g the set of available strategies in this way expands the set of outcomes (or sequences of outcomes) that can be sustained as e q u i l i b r i a. T h e existence of both cooperative and non-cooperative e q u i l i b r i a in repeated Prisoners' Dilemmas merely illustrates this fact.

both realism and neoliberalism provide us w i t h some hypotheses about how c o o r d i n a t i o n is achieved in international systems and w i t h the d i f f i c u l t y of coordination to different types of e q u i l i b r i a. It is those hypotheses to w h i c h we now turn.

3. C o o r d i n a t i o n M e c h a n i s m s and Regimes To assess the relevance of coordination to politics in general and to international processes in particular it is useful to consider the assumption c o m m o n l y employed to j u s t i f y the realist argument; namely, that "domestic systems are centralized and hierarchic ... International systems are decentralized and anarchic. T h e ordering principles of the two structures are d i s t i n c t l y different, indeed, contrary to each other" (Waltz 1979: 88). The specific issues we want to address here is whether domestic systems are, in p r i n c i p l e , any less anarchic than international systems, w h y the concept of power appears to be less central in domestic affairs, and whether the concept of coordination can be used to provide a more general understanding of p o l i t i c a l processes than we gain from other approaches (especially those that rely on some notion of power). We begin by noting that at one level we could attempt to account for p o l i c y outcomes i n , say, a democratic society by referring to the power of interest groups, of the media, of the courts versus the legislature, or of the legislature versus the executive. On closer inspection, h o w e v e r , we should f i n d that many of the things associated w i t h power or w i t h the determinants of power derive f r o m a political constitution, i m p l i c i t l y understood or e x p l i c i t l y written, that defines the state and the rules of "legitimate" p o l i t i c a l action. T h u s , understanding domestic politics in terms of a specific constellation of power requires that we understand why society's members i m p l i c i t l y or e x p l i c i t l y accede to the terms of a constitution that helps define and allocate power. Of course, although they are not necessarily concerned w i t h the concept of "power" per se, constitutional theorists are no less concerned w i t h the matter of endogenous enforcement — w i t h how a constitution's provisions are sustained and how a "piece of parchment" can contribute to p o l i t i c a l stability -- than are students of international affairs. The matter of the endogenous enforcement of constitutional provisions, like the issues that ostensibly separate realists and neoliberals, has been long debated o w i n g to the seemingly paradoxical requirement that stable constitutions enforce themselves. The essence of this paradox and the corresponding source of the temptation to account for stability in terms of power relations is revealed if we attempt to conceptualize a constitution as a contract l i k e the ones that set the terms of market exchanges (c.f., Brennan and Buchanan 1985). V i e w i n g a constitution thus necessarily leads to the question "Who or what enforces the contract?" w h i c h leads, in turn, to the search for the ultimate source of enforcement authority in society. B u t answering that the courts, the legislature, or the imperatives of electoral competition are the source of enforcement

merely pushes the p r o b l e m back a step so that we must ask: Who enforces the court's prerogatives, the legislature's j u r i s d i c t i o n , or the laws that regulate elections? At least at the constitutional level, then, states are no less anarchic in p r i n c i p l e than international systems in the sense that the ultimate source of domestic p o l i t i c a l stability must be endogenous. H o w e v e r , what makes domestic politics appear distinct f r o m international politics is that the mere fact of being a state requires that people achieve some m i n i m a l level of c o o r d i n a t i o n w i t h respect to the i m p l i c i t or e x p l i c i t rules of domestic social process. Without d e n y i n g the relevance of social norms, custom, and c u l t u r e , even if we restrict our attention to f o r m a l i z e d "democratic" rules, there are a great many alternative e q u i l i b r i a of rules. Thus the members of society must select one of these e q u i l i b r i a -- to establish a stable set of expectations about legitimate process today and in the future so that the mutual benefits of a stable and coherent p o l i t i c a l system can be realized. Written constitutions are a route to that end. It follows that constitutions are best conceptualized as mechanisms that help coordinate society to an e q u i l i b r i u m of rules ( H a r d i n 1988, Ordeshook 1992). A constitution is stable and s e l f - e n f o r c i n g if it establishes a set of s e l f - f u l f i l l i n g expectations about due process, about rights, and about legitimate ways of m a k i n g collective decisions. M o r e o v e r , c o n c e p t u a l i z i n g constitutions in this way forces us to see them as part of the "social fabric" that coordinates society in general — as part of the regime that describes society and the state -- and it leads to more practical questions such as " G i v e n the other things that can coordinate social action (e.g., e t h n i c i t y , r e l i g i o n , language), how do we craft rules to compete w i t h these things?" It is true that the salience of the issue of exogenous enforcement fades once a constitution becomes a stable part of society. At that point, students of domestic democratic politics can turn their attention to other matters such as the details of j u d i c i a l , legislative or electoral process without regard to how the rules s p e c i f y i n g the roles of the j u d i c i a r y , the legislature, or elections are ultimately enforced. H o w e v e r , l u r k i n g in the background is the fact that the rules d e f i n i n g these branches and their power constrain i n d i v i d u a l actions because acceptance of them describes some of the elements of social c o o r d i n a t i o n. Nevertheless, a realist might attempt to reassert the difference between international and stable domestic politics w i t h the argument that power dictates outcomes in pre- constitutional societies and that an international system is better described as such a society. C o r r e s p o n d i n g l y , restating Krasner's (1991) argument about the role of power in determining outcomes in the Battle of the Sexes, power rather than some i m p l i c i t adherence to rules, structures c o o r d i n a t i o n. H o w e v e r , aside from noting that we have never observed a "pure state of nature" in w h i c h people act on some basis other than beliefs about the actions of others in a w h o l l y uncoordinated fashion, suppose we ask how tyrants enforce their edicts. O u r first instinct may be to respond: " T h r o u g h c o e r c i o n administered by the m i l i t a r y or the police." But then we must ask: "Why

the e x - h e g e m o n may continue as the p r i m a r y instrument of international coordination long after it loses its status. On the other hand, what disappears w i t h the hegemon's relative decline is its ability to punish unilaterally and the expectation on the part of other states that it w i l l do so. T h u s , the decline of a hegemon before countries develop other devices that serve the same coordinative functions can greatly disrupt the ability of states to ensure continued adherence to the e q u i l i b r i u m that prevailed p r e v i o u s l y. In any event, the cooperative e q u i l i b r i a achieved under a hegemon w i l l be more susceptible to d i s r u p t i o n after a hegemon declines o w i n g to the f r a g i l i t y of beliefs. A n d it is at this point that the neoliberal offers the idea of "regime" as a coordination mechanism to substitute for to role of a hegemon. Indeed, the neoliberal's d e f i n i t i o n of a regime corresponds nearly i d e n t i c a l l y to such a mechanism -- "sets of i m p l i c i t or explicit principles, norms, rules, and d e c i s i o n - m a k i n g procedures around w h i c h actor's expectations converge" (Krasner 1983: 2), "a set of mutual expectations, rules and regulations, plans, organizational energies and f i n a n c i a l commitments, w h i c h have been accepted ..." ( R u g g i e 1975: 570), "recognized patterns of practice around w h i c h expectations converge" ( Y o u n g 1980: 337), and "rules of behavior that allow actor expectations to converge" (Stein 1982: 127). H e n c e , in a way that is w h o l l y consistent w i t h the requirements that game theory sets for a c h i e v i n g s p e c i f i c e q u i l i b r i a , neoliberalism places the study of regimes as c o o r d i n a t i o n mechanisms at the heart of international relations theory. H o w e v e r , it is important to understand that cooperative outcomes are o n l y one class of e q u i l i b r i a and that coordination can also i n v o l v e disputes over the selection of outcomes "along the Pareto frontier" — outcomes that may or may not entail overt conflict and that may or may not require an appeal to power and relative resources to discern f i n a l outcomes. T h u s , to the extent that the realist view can be interpreted as an argument about the "naturalness" of coordination to a class of e q u i l i b r i a other than the ones neoliberals envision as feasible, the debate between realists and neoliberals becomes a debate over the relative ease w i t h w h i c h states can coordinate to one e q u i l i b r i u m rather than another. That is, the dispute between realists and neoliberals is this: Realists argue that it is "more natural" to coordinate to non-cooperative e q u i l i b r i a (or to e q u i l i b r i a in w h i c h subsets of states -- alliances -- coordinate against other subsets) whereas neoliberals contend that institutions of various descriptions can effectively coordinate states to different (more u n i v e r s a l l y cooperative) outcomes.

4. W o r l d Orders as Alternative E q u i l i b r i a Of course, a mere restatement of the realist-neoliberal debate in terms of coordination cannot resolve matters. We now require an understanding of the comparative problems associated w i t h c o o r d i n a t i n g to the e q u i l i b r i a (world orders) that realists and neoliberals postulate, and, in particular, we must f i n d a way to formalize the meaning of "more natural" when speaking about the e q u i l i b r i a

in w h i c h states act as if they m a x i m i z e relative gain. That is, we should assess the argument that realist e q u i l i b r i a somehow impose fewer requirements on coordination than do the e q u i l i b r i a postulated by neoliberals. C o r r e s p o n d i n g l y , we also want to assess whether anarchic system can occasion e q u i l i b r i a in w h i c h power plays little or nor role in addition to e q u i l i b r i a in w h i c h power is the central concern of states. T h u s , we require an analysis that in p r i n c i p l e at least allows for the simultaneous existence of these e q u i l i b r i a , that informs us about the properties of the strategies that correspond to these e q u i l i b r i a when they exist, and, subsequently, that identifies the comparative advantages of coordinating to one of these e q u i l i b r i a rather than another. In searching for an appropriate theoretical sub-structure, we might begin once again w i t h the Prisoners' D i l e m m a. H o w e v e r , there are reasons for supposing that the this scenario cannot suit our purposes. F i r s t , even though Powell's (1991) analysis suggests that there may be routes around the problem, the usual representations of the repeated D i l e m m a does not allow for the e l i m i n a t i o n of states ( G r i e c o 1990). T h u s , the existence of universally cooperative e q u i l i b r i u m there cannot be interpreted as a solution to any "security dilemma" that states can confront. Second, unless we e x p l i c i t l y focus on n-person formulations and on strategies other that, say, T i t - f o r - T a t , the Prisoners' D i l e m m a can mislead us about the v i a b i l i t y of the neoliberal position. R e c a l l that analyses of the 2- person D i l e m m a focus on two e q u i l i b r i a -- a "cooperative" one in w h i c h all m u t u a l gains are realized through an e q u i l i b r i u m of T i t - f o r - T a t strategies and a "non-cooperative" one in w h i c h the players forego these gains and choose m y o p i c a l l y dominant strategies. Of these two e q u i l i b r i a , one is clearly more socially attractive than the other, so we might reasonably conjecture that c o o r d i n a t i o n to it can be realized without great d i f f i c u l t y. But the particular concern of realists is that there are other even more c o m p e l l i n g e q u i l i b r i a -- e q u i l i b r i a in w h i c h states pursue strategies that y i e l d antagonistic alliances designed to preclude the dominance of any single state (i.e., balance of power e q u i l i b r i a ). The issue, then, is not whether countries must choose between w h o l l y cooperative (e.g., collective security) e q u i l i b r i a and w h o l l y non-cooperative e q u i l i b r i a , but whether they can also cooperate by f o r m i n g competitive alliances.

These criticisms suggest that one approach is to consider n-person versions of the D i l e m m a , strategies that allow only subsets of players to cooperate, and models that somehow nest Prisoners' Dilemmas and Battle of the Sexes scenarios (Garrett 1992). H o w e v e r , rather than force any model into the straightjacket of particular scenarios, we should instead look at analyses that d i r e c t l y model the sources of conflict and cooperation, that allow for the elimination of countries, that allow for alliances, and that allow as well for cooperative e q u i l i b r i a in the form of, say, collective security arrangements that seek not only to ensure against conflict but that also are designed to realize the benefits of an efficient w o r l d economy. F o r these reasons it is useful to consider N i o u and

7. If the proposal is rejected, the o r i g i n a l threat is implemented -- thereby e l i m i n a t i n g the threatened country.
8. If the counter is accepted, it becomes the new current threat, and as in step 2, the threatened player m u c h choose either a new counter-threat or a resource transfer.

We note s i m p l y now that this 3-country game occasions two types of e q u i l i b r i a , w h i c h can be supported by the f o l l o w i n g (approximately described) strategies (notice that strategies specify what players do along the e q u i l i b r i u m path as well as what they should do if one or more players defect from that path):

E l : C o u n t r y 1, if given the first move, threatens (150,0,150); 2 threatens (0,150,150); 3 passes or threatens (150,0,150) or (0,150,150). If the i n i t i a l threat is (150,150,0), then "reject;" otherwise "accept." If threatened, states 1 or 2 transfer to the largest threatening country. If state 3 is threatened, then 3 offers (150,0,150) or (0,150,150) as a counter-threat. T h e e q u i l i b r i u m outcome here is an even chance lottery between (150,70,80) and (70,150,80).

E2: No state makes an i n i t i a l threat, but if one is offered, the proposed partner "rejects." If the i n i t i a l threat is rejected, then the "defecting" state is punished by being threatened in the next stage (and this threat is accepted). If two players defect by m a k i n g and accepting an i n i t i a l threat or by f a i l i n g to p u n i s h , then play the game as described in E1. T h e e q u i l i b r i u m outcome here is the i n i t i a l status quo, (120,100,80).

The first e q u i l i b r i u m corresponds to a pure conflict scenario in w h i c h a threat is made at the first opportunity and the threatened country, 1 or 2, survives only by "buying o f f the largest threatening country. No country is eliminated, but only because each has sufficient resources to make a "game ending" transfer and because no one wants to a l l o w anyone else to be predominant. Extensions of this analysis to n-countries reveals, moreover, that countries can be eliminated or can become more susceptible to being forced to make a resource transfer if their resources d i m i n i s h too greatly or if other states increase their resources too m u c h. Hence, in an E l - t y p e e q u i l i b r i u m , states are necessarily concerned w i t h power and relative gain. In contrast, the second e q u i l i b r i u m corresponds to an all-encompassing c o l l e c t i v e security system in w h i c h everyone agrees not to make an i n i t i a l threat and defectors are punished by the r e m a i n i n g countries. Notice that collective security here need not have a purely m i l i t a r y connotation -- it can refer also to various economic agreements that are enforced by punishment strategies a p p l i e d to those

who defect f r o m trade, monetary, or other such agreements. Whatever its interpretation, cooperation (in the f o r m of the absence of threats) is self-enforcing here, because punishments eliminate the benefits of defection and because administering those punishments is rational. In game-theoretic terms, this e q u i l i b r i u m is subgame perfect. We also want to emphasize that an E 2 - t y p e e q u i l i b r i u m exists regardless of the number of countries and regardless of the distribution of resources. It f o l l o w s , then, that in such an e q u i l i b r i u m states can pursue those subsidiary policies that generate mutual gains and, as in domestic p o l i t i c s , they can focus their attention on the construction of those institutional structures that regulate the Prisoners' D i l e m m a - t y p e scenarios that arise among states. Put s i m p l y , in an E 2 - t y p e e q u i l i b r i u m , states need not concern themselves w i t h relative gain at the expense of absolute gain. T h e situation that confronts the three countries in our example, then, is s u m m a r i z e d by G a m e 4, w h i c h illustrates the 3 - c o u n t r y game that results f r o m our scenario if each country must choose between p l a y i n g in accordance w i t h E1 or E 2. F o r example, if 1 chooses E1 and 2 and 3 play a c c o r d i n g to E 2 , then 1 defects (by offering an i n i t i a l threat), and 2 and 3 punish 1 and force 1 to transfer resources to 2. H e n c e , we enter (70,150,80) in cell ( E 1 , E 2 , E 2 ). In contrast, if 1 and 3 choose E1 but 2 chooses E 2 , then 1 and 3 threaten 2 and force a transfer to 1. H e n c e , we enter (150,70,80) in cell ( E 1 , E 2 , E 1 ). If 1 and 2 choose E1 but 3 chooses E 2 , then either 1 or 2 make an i n i t i a l threat (depending on w h o nature chooses first), 3 rejects, and the defector is punished so that either (150,70,80) or (70,150,80) prevails. Hence, we enter (110,100,80) in c e l l ( E 1 , E 1 , E 2 ).