A Property of Nash Equilibria in Repeated Games with Incomplete Information

We consider two-person non-zero-sum infinitely repeated games with lack of information on one side. The characterization of Nash equilibrium payoffs obtained by Hart allows for complex strategies, which are actually required by some equilibrium payoffs in some games. We show that appropriate one-shot public communication mechanisms make Nash equilibrium payoffs achievable by means of simple strategies. Furthermore, these mechanisms satisfy a notion of self-fulfillment.Journal of Economic LiteratureClassification Numbers: D82, C72.

[1]  Sylvain Sorin,et al.  Some results on the existence of Nash equilibria for non-zero sum games with incomplete information , 1983 .

[2]  Jonathan Shalev,et al.  Nonzero-Sum Two-Person Repeated Games with Incomplete Information and Known-Own Payoffs , 1994 .

[3]  F. Forges.  Repeated games of incomplete information: Non-zero-sum , 1992 .

[4]  Françoise Forges,et al.  Communication Equilibria in Repeated Games with Incomplete Information , 1988, Math. Oper. Res..

[5]  E. Minelli,et al.  Self-fulfilling mechanisms and rational expectations , 1997 .

[6]  David Armacost,et al.  Compactly cogenerated LCA groups , 1976 .

[7]  R. Simon,et al.  The existence of equilibria in certain games, separation for families of convex functions and a theorem of Borsuk-Ulam type , 1995 .

[8]  F. Forges,et al.  Equilibria with Communication in a Job Market Example , 1990 .

[9]  D. Blackwell.  An analog of the minimax theorem for vector payoffs. , 1956 .

[10]  Ehud Lehrer,et al.  Mediated talk , 1996 .

[11]  Shmuel Zamir,et al.  Repeated games of incomplete information: Zero-sum , 1992 .

[12]  Robert J. Aumann,et al.  Repeated Games with Incomplete Information , 1995 .

[13]  Sergiu Hart,et al.  Nonzero-Sum Two-Person Repeated Games with Incomplete Information , 1985, Math. Oper. Res..

[14]  Roger B. Myerson,et al.  Game theory - Analysis of Conflict , 1991 .

[15]  F. Forges,et al.  Correlated equilibria in a class of repeated games with incomplete information , 1985 .

[16]  Ehud Lehrer,et al.  One-Shot Public Mediated Talk , 1997 .

[17]  S. Hart,et al.  Bi-convexity and bi-martingales , 1986 .