## Abstract

The paper studies Bayesian games which are extended by adding pre-play communication. Let Γ be a Bayesian game with full support and with three or more players. The main result is that if players can send private messages to each other and make public announcements then every communication equilibrium outcome, q, that is rational (i.e., involves probabilities that are rational numbers) can be implemented in a sequential equilibrium of a cheap talk extension of Γ, provided that the following condition is satisfied: There exists a Bayesian Nash equilibrium s in Γ such that for each type t_{i} of each player i the expected payoff of t_{i} in q is larger than the expected payoff of t_{i} in s.

Original language | American English |
---|---|

Pages (from-to) | 45-71 |

Number of pages | 27 |

Journal | Journal of Economic Theory |

Volume | 108 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 2003 |

## Keywords

- Bayesian games
- Communication
- Sequential equilibrium