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Strategic information transmission with sender’s approval

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  • Renault, Jérôme
  • Forges, Françoise

Abstract

We consider a sender-receiver game with an outside option for the sender. After the cheap talk phase, the receiver makes a proposal to the sender, which the latter can reject. We study situations in which the sender’s approval is crucial to the receiver. We show that a partitional, (perfect Bayesian Nash) equilibrium exists if the sender has only two types or if the receiver’s preferences over decisions do not depend on the type of the sender as long as the latter participates. The result does not extend: we construct a counter-example (with three types for the sender and type-dependent affine utility functions) in which there is no mixed equilibrium. In the three type case, we provide a full characterization of (possibly mediated) equilibria.

Suggested Citation

  • Renault, Jérôme & Forges, Françoise, 2021. "Strategic information transmission with sender’s approval," TSE Working Papers 21-1216, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:125607
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    References listed on IDEAS

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    11. Ying Chen & Navin Kartik & Joel Sobel, 2008. "Selecting Cheap-Talk Equilibria," Econometrica, Econometric Society, vol. 76(1), pages 117-136, January.
    12. Jérôme Renault, 2001. "3-player repeated games with lack of information on one side," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 221-245.
    13. SORIN, Sylvain, 1983. "Some results on the existence of Nash equilibria for nonzero sum games with incomplete information," LIDAM Reprints CORE 553, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    15. Shimizu, Takashi, 2013. "Cheap talk with an exit option: The case of discrete action space," Economics Letters, Elsevier, vol. 120(3), pages 397-400.
    16. Takashi Shimizu, 2017. "Cheap talk with an exit option: a model of exit and voice," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1071-1088, November.
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    Cited by:

    1. Sémirat, Stéphan & Forges, Françoise, 2022. "Strategic information transmission with sender's approval: The single-crossing case," Games and Economic Behavior, Elsevier, vol. 134(C), pages 242-263.

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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C - Mathematical and Quantitative Methods

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