The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency

57 Pages Posted: 17 Sep 2013

See all articles by Dirk Bergemann

Dirk Bergemann

Yale University - Cowles Foundation - Department of Economics; Yale University - Cowles Foundation

Stephen Morris

Princeton University - Department of Economics

Multiple version iconThere are 3 versions of this paper

Date Written: September 16, 2013

Abstract

We define and characterize a notion of correlated equilibrium for games with incomplete information, which we call Bayes correlated equilibrium: The set of outcomes that can arise in Bayes Nash equilibria of an incomplete information game where players may have access to additional signals beyond the information structure is characterized and shown to be equivalent to the set of Bayes correlated equilibria.

A game of incomplete information can be decomposed into a basic game, given by actions sets and payoff functions, and an information structure. We introduce 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.

Keywords: correlated equilibrium, incomplete information, robust predictions, information structure, sufficiency, Blackwell ordering

JEL Classification: C72, D82, D83

Suggested Citation

Bergemann, Dirk and Morris, Stephen Edward, The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency (September 16, 2013). Economic Theory Center Working Paper No. 054-2013. Available at SSRN: https://ssrn.com/abstract=2327127 or http://dx.doi.org/10.2139/ssrn.2327127

Dirk Bergemann

Yale University - Cowles Foundation - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States
203-432-3592 (Phone)
203-432-2128 (Fax)

HOME PAGE: http://www.econ.yale.edu/~dirk/

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

Stephen Edward Morris (Contact Author)

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

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