Implementability of correlated and communication equilibrium outcomes in incomplete information games

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In a correlated equilibrium, the players' choice of actions is directed by correlated random messages received from an outside source, or mechanism. These messages allow for more equilibrium outcomes than without any messages (pure-strategy equilibrium) or with statistically independent ones (mixed-strategy equilibrium). In an incomplete information game, the messages may also reflect the types of the players, either because they are affected by extraneous factors that also affect the types (correlated equilibrium) or because the players themselves report their types to the mechanism (communication equilibrium). Mechanisms may be further differentiated by the connections between the messages that the players receive and their own and the other players' types, by whether the messages are statistically dependent or independent, and by whether they are random or deterministic. Consequently, whereas for complete information games there are only three classes of equilibrium outcomes, with incomplete information the corresponding number is 14 or 15 for correlated equilibria and even larger-15, 16 or 17-for communication equilibria. For both solution concepts, the implication relations between the different kinds of equilibria form a two-dimensional lattice, which is considerably more intricate than the single-dimensional one of the complete information case.

Original languageEnglish
Pages (from-to)283-350
Number of pages68
JournalInternational Journal of Game Theory
Issue number2
StatePublished - May 2014


  • Bayesian games
  • Communication equilibrium
  • Correlated equilibrium
  • Implementation
  • Incomplete information
  • Mechanism


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