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Envy driven equilibrium in single peaked, single crossing, cheap talk games

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  • Stéphan Sémirat

    (GAEL - Laboratoire d'Economie Appliquée de Grenoble - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

Abstract

Forges and Renauld (2021) consider a Sender-Receiver game with finitely many types, in which a proposal phase is added after the cheap talk phase, allowing the Sender to exit if she does not approve the proposal. The authors give various sufficient conditions for the existence of a PBE without exit (e.g.: the Sender has only two types, or the Receiver's utility is type-independent, or the Sender's utility is monotonic in the Receiver's decision). We extend the result to the setting in which utility functions are concave, single peaked and single crossing. We propose a constructive algorithm that always achieve a PBE without exit. The algorithms starts from the fully revealing strategy. At that step, individual rationality obtains easily. Then the algorithm gradually reaches incentive compatibility, while keeping individual rationality, by merging any envying type with the types he envies. At least when the IR condition is irrelevant (as in most applications), the algorithm turns out to reach a unique PBE. Moreover,the reached PBE is maximal with respect to the number of information cells.

Suggested Citation

  • Stéphan Sémirat, 2021. "Envy driven equilibrium in single peaked, single crossing, cheap talk games," Post-Print hal-03531626, HAL.
    • Handle: RePEc:hal:journl:hal-03531626
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    Keywords

    Selecting cheap; Talk equilibria;

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