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Timing of Messages and the Aumann Conjecture: A multiple-Selves Approach

Author

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  • Roi Zultan

    (Department of Economics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel)

Abstract
The Aumann (1990) conjecture states that cheap-talk messages do not necessarily help to coordinate on efficient Nash equilibria. In an experimental test of Aumann’s conjecture, Charness (2000) found that cheap-talk messages facilitate coordination when they precede the action, but not when they follow the action. Standard game-theoretical modeling abstracts from this timing effect, and therefore cannot account for it. To allow for a formal analysis of the timing effect, I study the sequential equilibria of the signaling game in which the sender is modeled as comprising two selves: an acting self and a signaling self. I interpret Aumann’s argument in this context to imply that all of the equilibria in this game are ‘babbling’ equilibria, in which the message conveys no information and does not affect the behavior of the receiver. Using this framework, I show that a fully communicative equilibrium exists—only if the message precedes the action but not when the message follows the action. In the latter case, no information is transmitted in any equilibrium. This result provides a game-theoretical explanation for the puzzling experimental results obtained by Charness (2000). I discuss other explanations for this timing-of-message effect and their relationship to the current analysis.

Suggested Citation

  • Roi Zultan, 2011. "Timing of Messages and the Aumann Conjecture: A multiple-Selves Approach," Working Papers 1109, Ben-Gurion University of the Negev, Department of Economics.
    • Handle: RePEc:bgu:wpaper:1109
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    References listed on IDEAS

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    Cited by:

    1. Karl H. Schlag & Péter Vida, 2021. "Believing when credible: talking about future intentions and past actions," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 867-889, December.
    2. Sobel, Joel, 2017. "A note on pre-play communication," Games and Economic Behavior, Elsevier, vol. 102(C), pages 477-486.
    3. Schlag, Karl H. & Vida, Péter, 2013. "Commitments, Intentions, Truth and Nash Equilibria," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 438, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    4. Sobel, Joel, 2017. "A note on pre-play communication," University of California at San Diego, Economics Working Paper Series qt68d1t1xg, Department of Economics, UC San Diego.

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    More about this item

    Keywords

    pre-play communication; Nash equilibrium; coordination games; multiple selves;
    All these keywords.

    JEL classification:

    • A13 - General Economics and Teaching - - General Economics - - - Relation of Economics to Social Values
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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