Bayes Correlated Equilibrium and the Comparison of Information Structures

The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may or may not have access to more private information is characterized and shown to be equivalent to the set of an incomplete information version of correlated equilibrium, which we call Bayes correlated equilibrium. We describe a partial order on many player information structures -- which we call individual sufficiency -- under which more information shrinks the set of Bayes correlated equilibria. We discuss the relation of the solution concept to alternative definitions of correlated equilibrium in incomplete information games and of the partial order on information structures to others, including Blackwell's for the single player case.

[1]  F. Forges,et al.  Communication equilibria with partially verifiable types , 2005 .

[2]  R. Myerson.  Optimal coordination mechanisms in generalized principal–agent problems , 1982 .

[3]  E. Torgersen.  Comparison of Statistical Experiments , 1991 .

[4]  Jeffrey C. Ely,et al.  Hierarchies of Belief and Interim Rationalizability , 2004 .

[5]  J. Marschak,et al.  ECONOMIC COMPARABILITY OF INFORMATION SYSTEMS. , 1968 .

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

[7]  R. Aumann.  Subjectivity and Correlation in Randomized Strategies , 1974 .

[8]  J. Mertens,et al.  The Value of Information in Zero-Sum Games , 2001 .

[9]  Qingmin Liu.  Correlation and Common Priors in Games with Incomplete Information , 2011 .

[10]  Andrew Caplin,et al.  A Testable Theory of Imperfect Perception , 2011 .

[11]  J. Hirshleifer.  The Private and Social Value of Information and the Reward to Inventive Activity , 1971 .

[12]  Abraham Neyman.  The Positive Value of Information , 1991 .

[13]  F. Forges.  Correlated Equilibrium in Games with Incomplete Information Revisited , 2006 .

[14]  Kevin D. Cotter.  Correlated equilibrium in games with type-dependent strategies , 1991 .

[15]  Marcin Peski.  Comparison of information structures in zero-sum games , 2008, Games Econ. Behav..

[16]  R. Aumann.  Correlated Equilibrium as an Expression of Bayesian Rationality Author ( s ) , 1987 .

[17]  D. Bergemann,et al.  Robust Mechanism Design , 2003 .

[18]  Olivier Gossner,et al.  Comparison of Information Structures , 2000, Games Econ. Behav..

[19]  D. Blackwell.  Comparison of Experiments , 1951 .

[20]  Ehud Lehrer,et al.  Signaling and Mediation in Games with Common Interests , 2006, Games Econ. Behav..