PREFACE

The potentialities of game theory as a tool of mathematicized social science were widely discussed as soon as the theory made its appearance. In the beginning, the predominant expectations were centered on the development of a strategic theory, that is, one which aims to single out from a set of possible courses of action an optimal one in the sense of according the greatest advantage to an actor, whose interests conflict with those of other actors. In fact, the so called Fundamental Theorem of Game Theory, proved by J. Von Neumann in 1928, established the existence of 'optimal strategies' in this sense in the context of the two-person constantsum game, the idealized model of two-sided conflict where the interests of the two players are diametricaUy opposed. Many-sided conflicts are, o f course, commonplace in real life, and it seemed natural to expect that extensions of the theory to n-person games would shed light on the nature of 'optimal strategies' (again from the point of view of a given player) in such situations. However, the extension of the idea of 'optimal strategy' to n-person games turned out to be by no means straightforward. Whereas in the two-person constantsum game, the meaning of 'optimal strategy' derives naturally from the concept of an equilibrium, in the n-person game it does not. In the two-person constantsum game, if both players choose strategies that contain equilibrium outcomes, the resulting outcome must be an equilibrium, but in n-person games this is not necessarily the case. (It is also not necessarily the case in two-person non-constantsum games.) It follows that to secure an equilibrium outcome in an n-person game (or a two person non-constantsum game), the strategies of the players must be coordinated. That is to say, it is in general impossible to secure such an outcome by advising each player to choose a strategy independent of the other player's choices. (It is possible to do so in a two-person constantsurn game.) And so the game theorist in the role of consultant must act as a 'coordinator' of strategic choices of the players. 'To what purpose?' one might ask. To secure an equilibrium outcome. But what is special about equilibrium outTheory and Decision 8 (1977) 1--4. All Rights Reserved Copyright @ 1977 by D. Reidel Publishing Company, Dordrecht-Holland

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comes? To this one might reply that equilibrium outcomes are natural candidates for 'rational' outcomes because they are 'selfenforcing'. By definition of equilibrium, no player can gain an advantage by unilaterally shifting away from an equilibrium. For this reason, equilibria have been singled out as solutions of non-cooperative games, where communication or negotiation with or without side payments among the players are not possible. However, once the coordination of strategies is admitted to the conceptual repertoire of game theory, the next step naturally suggests itself, namely the coordination of strategies to attain not merely a selfenforcing but a collectively rational outcome. Such are Pareto-optimal outcomes, those that cannot be 'collectively improved upon'. Pareto-optimal outcomes are the nexus between the coicident and the conflicting interests of the players. All players prefer Pareto-optimal outcomes to non-Pareto-optimal ones. Their interests conflict in the sense that among the Pareto-optimal outcomes those that are more advantageous to some players must be less disadvantageous to others. In general, Pareto-optimal outcomes are not equilibria and so are not self-enforcing. To attain them some agreement among the players is required, enforceable either by externally imposed sanctions or by internal commitments of the players. To the extent that special sets of Pareto-optimal outcomes are singled out as 'solutions' or cooperative games, game theory enters the role of a theory of conflict resolution. The game is conceived as a conflict to be resolved rather than conducted from the standpoint of advantages accruing to a single player or a particular proper subset of players. It seems to the editor that in this role game theory can make more constructive contributions to social science than in its original conception as a theory of optimal strategic choices. The present issue and the next continue the themes developed in Game Theory as a Theory of Conflict Resolution (Dordrecht: D. Reidel Publishing Co., 1974). The eight papers fall into three categories. Those by Bergstrasser and Yu, by Cyert and De Groot, and by Kilgour are in the tradition of mathematical game theory proper; that is, they examine the structure of n-person cooperative games, specifically the structure of the numerous solution concepts (Bergstrasser and Yu), of a generalized Shapley Value (Kilgour), and of a situation with dual control, which constitutes a two-person non-constantsum game in dynamic form (Cyert and De Groot). Three papers deal with experimental tests of solutions of cooperative games, namely, n-person games in characteristic function form (Horowitz, Kahan and Am. Rapoport), two-

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person non-constantsum games (An. Rapoport, Frenkel and Perner). The remaining two papers by Cassidy and Neave and by Friend, Laing, and Morrison deal with theoretical models of coalition formation and experimental tests of these models. The theory of coalition formation has been rather neglected by game theoreticians, probably because it is difficult to incorporate this process into normative (prescriptive) static models, which constitute the bulk of game theory. For example, if an n-person game is given in classical (superadditive) characteristic function form, with side payments, the principle of collective rationality implies that the coalition which can attain the largest joint payoff should form. In general, this would be the grand coalition of all n-players. To be sure, if sets of imputations are singled out as solutions, these would be determined by the values of the game to coalitions that could form, since these potential coalitions determine the bargaining positions of the players. But these potential coalitions are analogous to the transient states in a dynamic process (which classical n-person game theory does not examine). The end state in these approaches is typically the grand coalition, as implied by the requirement that the sum of the payoffs in an imputation be equal to the value of the game to the grand coalition. Other approaches, e.g., those leading to the bargaining set or the kernel solutions, examine payoffs configurations that are 'stable' when associated with a particular given coalition structure. To raise the question which coalition structure is likely to form is to shift the emphasis from normative to descriptive aspects of the theory. This is done in Friend, Laing, and Morrison's paper. In the case of Cassidy and Neaves' paper, the prescriptive focus is kept but in the context of strategic considerations of individual players, a throw-back to the original focus of game theory. One might, therefore, raise the question of whether the two papers on coalition formation do not fall outside the theme of this issue. Their inclusion can be justified by the necessity of examining the actual dynamics of conflict (to be sure in strictly controlled laboratory conditions), where opportunities for coalitions exist and where players are guided by competitive pressures, before proposing theories of conflict resolution based on collective rationality. Kilgour's paper should also be read in the same spirit. 'Quarreling' is certainly not part of a prescriptive theory of conflict resolution, where the conflict is between a priori specified interests. Rather quarrels, in the sense

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of foreclosing the formation of certain coalitions, are simply a condition introduced as a 'fact o f life' in order to see how the normative Shapley Value solutions of n-person games are affected by circumstances of this sort. ANATOL RAPOPORT