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Generic Finiteness of Equilibrium Outcome Distributions in Sender-Received Cheap-Talk Games

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  • In-Uck Park

    (University of Bristol)

Abstract

This paper establishes the generic finiteness of equilibrium outcome distributions for Sender-Receiver cheap-talk games. An equilibrium in a Sender-Receiver cheap-talk game is said to be in reduced form if every message is used by at least one type and no two messages provoke the same response. It is shown that, for a generic set of utilities on outcomes, a Sender-Receiver cheap-talk game has a finite number of reduced form equilibria. A corollary is that, for generic utilities, the set of probability distributions over outcomes generated by equilibria is finite. Because of the identification of terminal nodes for utility purposes, Sard's theorem is not applicable in the way it was used in Kreps and Wilson (1982), and a structurally different proof strategy is developed. Some additional characterization of the equilibria are obtained in the process of the proof.

Suggested Citation

  • In-Uck Park, 1993. "Generic Finiteness of Equilibrium Outcome Distributions in Sender-Received Cheap-Talk Games," Game Theory and Information 9310002, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:9310002
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    References listed on IDEAS

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    1. Govindan, Srihari & McLennan, Andrew, 2001. "On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms," Econometrica, Econometric Society, vol. 69(2), pages 455-471, March.
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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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