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

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  • Dirk Bergemann
  • Stephen Morris

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.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000730.

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Date of creation: 19 Sep 2013
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Handle: RePEc:cla:levarc:786969000000000730

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  1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
  2. Neyman, Abraham, 1991. "The positive value of information," Games and Economic Behavior, Elsevier, vol. 3(3), pages 350-355, August.
  3. R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
  4. Andrew Caplin & Daniel Martin, 2013. "A Testable Theory of Imperfect Perception," Levine's Working Paper Archive 786969000000000649, David K. Levine.
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