CFDP 1909R

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


Publication Date: September 2013

Revision Date: May 2014

Pages: 56


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 given information structure is characterized and shown to be equivalent to the set of a version of incomplete information correlated equilibria which we dub 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.


Correlated equilibrium, Incomplete information, Robust predictions, Information structure, Sufficiency, Blackwell ordering

JEL Classification Codes:  C72, D82, D83