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Sequential Equilibria in Bayesian Games with Communication

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Abstract

We study the effects of communication in Bayesian games when the players are sequentially rational but some combinations of types have zero probability. Not all communication equilibria can be implemented as sequential equilibria. We define the set of strong sequential equilibria (SSCE) and characterize it. SSCE differs from the concept of sequential communication equilibrium (SCE) defined by Myerson (1986) in that SCE allows the possibility of trembles by the mediator. We show that these two concepts coincide when there are three or more players, but the set of SSCE may be strictly smaller than the set of SCE for two-player games.

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  • Dino Gerardi & Roger B. Myerson, 2005. "Sequential Equilibria in Bayesian Games with Communication," Cowles Foundation Discussion Papers 1542, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1542
    Note: CFP 1237.
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d15/d1542.pdf
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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
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    7. Amparo Urbano & Jose E. Vila, 2002. "Computational Complexity and Communication: Coordination in Two-Player Games," Econometrica, Econometric Society, vol. 70(5), pages 1893-1927, September.
    8. Ben-Porath, Elchanan, 2003. "Cheap talk in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 108(1), pages 45-71, January.
    9. Gerardi, Dino, 2004. "Unmediated communication in games with complete and incomplete information," Journal of Economic Theory, Elsevier, vol. 114(1), pages 104-131, January.
    10. Dhillon, Amrita & Mertens, Jean Francois, 1996. "Perfect Correlated Equilibria," Journal of Economic Theory, Elsevier, vol. 68(2), pages 279-302, February.
    11. Myerson, Roger B, 1986. "Multistage Games with Communication," Econometrica, Econometric Society, vol. 54(2), pages 323-358, March.
    12. Imre Bárány, 1992. "Fair Distribution Protocols or How the Players Replace Fortune," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 327-340, May.
    13. Ben-Porath, Elchanan, 1998. "Correlation without Mediation: Expanding the Set of Equilibrium Outcomes by "Cheap" Pre-play Procedures," Journal of Economic Theory, Elsevier, vol. 80(1), pages 108-122, May.
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    Cited by:

    1. Balzer, Benjamin & Schneider, Johannes, 2021. "Persuading to participate: Coordination on a standard," International Journal of Industrial Organization, Elsevier, vol. 78(C).
    2. Sebastian Schweighofer-Kodritsch & Roland Strausz, 2023. "Principled Mechanism Design with Evidence," Berlin School of Economics Discussion Papers 0030, Berlin School of Economics.
    3. Izmalkov, Sergei & Lepinski, Matt & Micali, Silvio, 2011. "Perfect implementation," Games and Economic Behavior, Elsevier, vol. 71(1), pages 121-140, January.
    4. Benjamin Balzer & Johannes Schneider, 2022. "Mechanism Design with Informational Punishment," Papers 2201.01149, arXiv.org, revised Aug 2022.
    5. Correia-da-Silva, João, 2020. "Self-rejecting mechanisms," Games and Economic Behavior, Elsevier, vol. 120(C), pages 434-457.
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    7. Balzer, Benjamin & Schneider, Johannes, 2023. "Mechanism design with informational punishment," Games and Economic Behavior, Elsevier, vol. 140(C), pages 197-209.
    8. Sergei Izmalkov & Matt Lepinski & Silvio Micali, 2010. "Perfect Implementation," Working Papers w0140, New Economic School (NES).
    9. Dai Zusai, 2012. "Excess Liquidity against Predation," DETU Working Papers 1201, Department of Economics, Temple University.

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    More about this item

    Keywords

    Bayesian games; Communication; Communication equilibrium; Sequential communication equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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