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Strategic information transmission with sender's approval

Author

Listed:
  • Françoise Forges

    (LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres)

  • Jérôme Renault

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique, UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse)

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

  • Françoise Forges & Jérôme Renault, 2021. "Strategic information transmission with sender's approval," Post-Print hal-02440627, HAL.
    • Handle: RePEc:hal:journl:hal-02440627
    DOI: 10.1007/s00182-021-00757-1
    Note: View the original document on HAL open archive server: https://hal.science/hal-02440627
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    References listed on IDEAS

    as
    1. Olivier Compte & Philippe Jehiel, 2009. "Veto Constraint in Mechanism Design: Inefficiency with Correlated Types," American Economic Journal: Microeconomics, American Economic Association, vol. 1(1), pages 182-206, February.
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    4. Forges, Francoise, 1990. "Universal Mechanisms," Econometrica, Econometric Society, vol. 58(6), pages 1341-1364, November.
    5. Forges, Françoise & Horst, Ulrich, 2018. "Sender–receiver games with cooperation," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 52-61.
    6. Bester, Helmut & Strausz, Roland, 2001. "Contracting with Imperfect Commitment and the Revelation Principle: The Single Agent Case," Econometrica, Econometric Society, vol. 69(4), pages 1077-1098, July.
    7. Philippe Jehiel & Olivier Compte, 2007. "On Quitting Rights in Mechanism Design," American Economic Review, American Economic Association, vol. 97(2), pages 137-141, May.
    8. Steven A. Matthews, 1989. "Veto Threats: Rhetoric in a Bargaining Game," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(2), pages 347-369.
    9. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    10. Matthews, Steven A. & Postlewaite, Andrew, 1989. "Pre-play communication in two-person sealed-bid double auctions," Journal of Economic Theory, Elsevier, vol. 48(1), pages 238-263, June.
    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).
    14. repec:dau:papers:123456789/6109 is not listed on IDEAS
    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.
    17. Gresik, Thomas A., 1991. "Ex ante efficient, ex post individually rational trade," Journal of Economic Theory, Elsevier, vol. 53(1), pages 131-145, February.
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    Full references (including those not matched with items on IDEAS)

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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

    Keywords

    Approval; Cheap talk; Sender–receiver game; Participation constraints;
    All these keywords.

    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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