Bayes Correlated Equilibrium and the Comparison of Information Structures in Games

40 Pages Posted: 16 Apr 2015

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 2 versions of this paper

Date Written: April 15, 2015

Abstract

A game of incomplete information can be decomposed into a basic game and an information structure. The basic game defines the set of actions, the set of payoff states the payoff functions and the common prior over the payoff states. The information structure refers to the signals that the players receive in the game.

We characterize the set of outcomes that can arise in Bayes Nash equilibrium if players observe the given information structure but may also observe additional signals. The characterization corresponds to the set of (a version of) incomplete information correlated equilibria which we dub Bayes correlated equilibria.

We identify a partial order on many player information structures (individual sufficiency) under which more information shrinks the set of Bayes correlated equilibria. This order captures the role of information in imposing (incentive) constraints on behavior.

Keywords: Correlated equilibrium, Incomplete information, Bayes Nash equilibrium, Bayes correlated equilibrium, Robust predictions, Information structure, Sufficiency, Blackwell ordering

JEL Classification: C72, D82, D83

Suggested Citation

Bergemann, Dirk and Morris, Stephen Edward, Bayes Correlated Equilibrium and the Comparison of Information Structures in Games (April 15, 2015). Cowles Foundation Discussion Paper No. 1909RRR. Available at SSRN: https://ssrn.com/abstract=2594822 or http://dx.doi.org/10.2139/ssrn.2594822

Dirk Bergemann (Contact Author)

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

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States

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