Russian Contributions to Game Theory and Equilibrium Theory (Theory and Decision Library C Book 39)

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. Introduction....Pages 1-17 Front Matter....Pages 19-19 A probabilistic model of social choice....Pages 21-32 Equilibrium points in general noncooperative games and their mixed extensions....Pages 33-56 On the theory of optimality principles for noncooperative games....Pages 57-75 Front Matter....Pages 77-77 A sufficient condition for the coincidence of the core of a cooperative game with its solution....Pages 79-81 On the Shapley function for games with an infinite number of players....Pages 83-89 Cores and generalized NM-solutions for some classes of cooperative games....Pages 91-149 Front Matter....Pages 151-151 The linear bargaining solution....Pages 153-164 On the superlinear bargaining solution....Pages 165-174 Stable compromises under corrupt arbitration....Pages 175-178 Front Matter....Pages 179-179 Stability of economic equilibrium....Pages 181-215 An algorithmic approach for searching an equilibrium in fixed budget exchange models....Pages 217-235 Equilibrated states and theorems on the core....Pages 237-250

the Research Of Soviet Scientists Within The Field Of Game Theory, Starting Around 1965 Under The Supervision Of N. N. Vorob`ev, One Of The Leading Experts In The Field, Has Resulted In Many High-level Publications. The Purpose Of This Book Is To Report About The Highly Qualified Research By Russian Game Theorists During The Two Decades 1968 - 1988 To The International Readership. The Book Contains 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 About The Development Of Game Theory In The Ussr Before 1990 Is Given In The Introduction.

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. The research of Soviet scientists within the field of game theory has resulted in many high-level publications. This book aims to report about the research by Russian game theorists during the two decades 1968 - 1988 to the international readership. It contains a collection of contributions in game theory and the field of equilibrium theory