ENGINEERING COOPERATION IN TWO-PLAYER GAMES DRAFT SEP 28 , 2009

Selfish, strategic players may benefit from cooperation, provided they reach an agreement. It is therefore important to construct mechanisms that enable such cooperation, especially in the case of asymmetric private information. There are two major issues: (1) the determination of a fair and efficient outcome among the many compromises possible in a strategic game, and (2) the establishment of a play protocol under which strategic players will agree to the selected compromise. The paper presents a general solution for an important class of two person Bayesian games with monetary payoffs. The proposed solution builds on earlier concepts in game theory. It coincides with the von Neumann minmax value on the class of zero sum games and with the major solution concepts to the Nash Bargaining Problem. Moreover the solution is based on a simple decomposition of every game into cooperative and competitive components, which is easy to compute.

[1]  Ehud Lehrer,et al.  Evaluating Information in Zero-Sum Games with Incomplete Information on Both Sides , 2010, Math. Oper. Res..

[2]  Ananish Chaudhuri.  Experiments in Economics : Playing fair with money , 2009 .

[3]  Paul W. Goldberg,et al.  The complexity of computing a Nash equilibrium , 2006, STOC '06.

[4]  Ignacio García-Jurado,et al.  The Shapley Valuation Function for Strategic Games in which Players Cooperate , 2006, Math. Methods Oper. Res..

[5]  Xi Chen,et al.  Computing Nash Equilibria: Approximation and Smoothed Complexity , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[6]  Matthew O. Jackson,et al.  Endogenous games and mechanisms: Side payments among players , 2005 .

[7]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..

[8]  C. Mezzetti.  Mechanism Design with Interdependent Valuations: Efficiency , 2004 .

[9]  Colin Camerer.  Behavioral Game Theory: Experiments in Strategic Interaction , 2003 .

[10]  Ignacio García-Jurado,et al.  Values for strategic games in which players cooperate , 2003, Int. J. Game Theory.

[11]  Geoffroy de Clippel,et al.  Two-person bargaining with verifiable information , 2002 .

[12]  Françoise Forges,et al.  The ex ante incentive compatible core in the absence of wealth effects , 2002 .

[13]  Matthew O. Jackson,et al.  A crash course in implementation theory , 2001, Soc. Choice Welf..

[14]  E. Fehr.  A Theory of Fairness, Competition and Cooperation , 1998 .

[15]  Yair Tauman,et al.  On the value of information in a strategic conflict , 1990 .

[16]  Eitan Zemel,et al.  Nash and correlated equilibria: Some complexity considerations , 1989 .

[17]  L. Shapley.  A Value for n-person Games , 1988 .

[18]  Robert B. Wilson.  Game-Theoretic Analysis of Trading Processes. , 1985 .

[19]  M. Satterthwaite,et al.  Efficient Mechanisms for Bilateral Trading , 1983 .

[20]  R. Myerson.  Two-Person Bargaining Problems with Incomplete Information , 1982 .

[21]  R. Myerson,et al.  Monotonicity and independence axioms , 1980 .

[22]  E. Kalai,et al.  Arbitration of two-party disputes under ignorance , 1978 .

[23]  E. Kalai.  Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons , 1977 .

[24]  Robert W. Rosenthal,et al.  An Arbitration Model for Normal-Form Games , 1976, Math. Oper. Res..

[25]  E. Kalai,et al.  OTHER SOLUTIONS TO NASH'S BARGAINING PROBLEM , 1975 .

[26]  R. Aumann.  The core of a cooperative game without side payments , 1961 .

[27]  H. Raiffa.  21. Arbitration Schemes for Generalized Two-person Games , 1953 .

[28]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[29]  J. Neumann.  Zur Theorie der Gesellschaftsspiele , 1928 .

[30]  M. Rabin.  Published by: American , 2022 .

[31]  J. G. Pierce,et al.  Geometric Algorithms and Combinatorial Optimization , 2016 .

[32]  A. Roth.  Axiomatic models of bargaining , 1979 .

[33]  M. Bacharach.  Two-person Cooperative Games , 1976 .

[34]  J. Harsanyi.  Games with Incomplete Information Played by “Bayesian” Players Part II. Bayesian Equilibrium Points , 1968 .

[35]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.