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

  • Roi Zultan

    ()

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

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.

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Paper provided by Ben-Gurion University of the Negev, Department of Economics in its series Working Papers with number 1109.

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Length: 15 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:bgu:wpaper:1109
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