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Undefeated equilibrium and better response dynamics in sender receiver games

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  • Stéphan Sémirat

    (UGA - Université Grenoble Alpes, 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

We study pure perfect Bayesian equilibria (PBE) in sender-receiver games with finitely many types for the sender. Such equilibria are characterized by incentive compatible (IC) partitions of the sender's types. To refine PBE, we define forward neologism-proof (FNP) IC partitions, a variant of Farrell's neologism proof equilibrium. In the case of real-valued decisions and well-behaved utility functions (namely, strictly concave, single-peaked, with an upward bias for the sender and single-crossing w.r.t. a given order over the types), we propose a family of algorithms that all converge to a unique FNP IC partition, which establishes existence of a FNPE in our framework. While our refinement (like many other ones) starts from a supposedly played equilibrium and takes account of the incentives of some types to separate off path from the types they are pooled with, the algorithms take the opposite direction. Starting from a fully separating sender's strategy, types are gradually pooled as long as some of them envy decisions associated with other types.

Suggested Citation

  • Stéphan Sémirat, 2024. "Undefeated equilibrium and better response dynamics in sender receiver games," Post-Print hal-04700854, HAL.
    • Handle: RePEc:hal:journl:hal-04700854
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    Keywords

    Cheap talk game; undefeated equilibrium;

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