Russian Contributions to Game Theory and Equilibrium Theory

V.A. Vasil'ev and E.B. Yanovskaya 1 Game theory in the USSR before 1990 In this introductory chapter ?rst a short historical information about the development of game theory in the USSR before the 1990s is given. It should help to understand the choice of the papers in this volume. The development of game theory in the USSR began in the early sixties. N.N.Vorob'ev (1925- 1995) was the author of the ?rst papers about game theory in Russian; he was also the leader of a group of PhD students and young researchers at Leningrad who studied this new ?eldinmathematics. The early papers by Vorob'ev on enumerating equilibrium points in - matrix games ([74]), coalitional games where a player may belong to di erent coalitions ([77] and [78]) and equivalence of di erent types of strategies in games in extensive form ([75] and [76]), were published in Soviet journals having English translations, and so they became known in the West. Later on, game theory in the USSR exhibited signi?cant progress, which deserved world-wide attention. However, many game-theoretic papers were published in Soviet journals and edited volumes which have never been translated into English. In the 1960s, the theory of zero-sum games was popular in the USSR.

Classical Russian literature on Game Theory, up to now only published in Russian language Fills the informational gap in game-theoretic results obtained in the former Soviet Union between 1968 and 1988 Includes supplementary material: sn.pub/extras

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The purpose of this book is to report to the international readership on the sophisticated research by Russian game theorists during the two decades 1968 - 1988. The book includes a collection of contributions in game theory and the related field of equilibrium theory which never had been published in English before. A short historical survey on the development of game theory in the USSR before 1990 is given in the introduction.

Contenu
Sufficient conditions for existence of Mi1-bargaining sets.- Noncooperative game theory and social choice.- A probabilistic model of social choice.- Equilibrium points in general noncooperative games and their mixed extensions.- On the theory of optimality principles for noncooperative games.- Cooperative game theory.- A sufficient condition for the coincidence of the core of a cooperative game with its solution.- On the Shapley function for games with an infinite number of players.- Cores and generalized NM-solutions for some classes of cooperative games.- Bargaining theory.- The linear bargaining solution.- On the superlinear bargaining solution.- Stable compromises under corrupt arbitration.- Equilibrium theory.- Stability of economic equilibrium.- An algorithmic approach for searching an equilibrium in fixed budget exchange models.- Equilibrated states and theorems on the core.