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Noisy Talk

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Abstract

We examine the possibilities for communication between agents with divergent preferences in a noisy environment. Taking Crawford and Sobel's [4] (noiseless) communication game as a reference point, we study a model in which there is a probability epsilon in (0, 1) that the received message is a random draw from the entire message space, independent of the actual message sent by the sender. Just as in the CS model, we find that all equilibria are interval partitional; but unlike in CS, coding (the proportion of the message space used by any given set of types) is of critical importance. Via the appropriate coding scheme, one can construct equilibria that induce finitely many, a countable infinity or even an uncountable infinity of actions. Furthermore, for a given number of actions, there is typically a continuum of equilibria that induce that many actions. Surprisingly, the possibility of error can improve the prospects for communication. We show that for small noise levels there is a simple class of equilibria that are almost always welfare superior to the best CS equilibrium. There exists an optimal noise level for which these equilibria achieve the efficiency bound for general communication devices. Furthermore, for a range of biases introducing any amount of noise can be beneficial.

Suggested Citation

  • Andreas Blume & Oliver Board & Kohei Kawamura, 2007. "Noisy Talk," ESE Discussion Papers 167, Edinburgh School of Economics, University of Edinburgh.
  • Handle: RePEc:edn:esedps:167
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    References listed on IDEAS

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    1. Austen-Smith, David, 1994. "Strategic Transmission of Costly Information," Econometrica, Econometric Society, vol. 62(4), pages 955-963, July.
    2. Navin Kartik, 2005. "Information Transmission with Cheap and Almost-Cheap Talk," NajEcon Working Paper Reviews 666156000000000650, www.najecon.org.
    3. Morgan, John & Stocken, Phillip C, 2003. " An Analysis of Stock Recommendations," RAND Journal of Economics, The RAND Corporation, vol. 34(1), pages 183-203, Spring.
    4. Goltsman, Maria & Hörner, Johannes & Pavlov, Gregory & Squintani, Francesco, 2009. "Mediation, arbitration and negotiation," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1397-1420, July.
    5. Robert J. Aumann & Sergiu Hart, 2003. "Long Cheap Talk," Econometrica, Econometric Society, vol. 71(6), pages 1619-1660, November.
      • Robert J. Aumann & Sergiu Hart, 2002. "Long Cheap Talk," Discussion Paper Series dp284, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised Nov 2002.
    6. Kovác, Eugen & Mylovanov, Tymofiy, 2009. "Stochastic mechanisms in settings without monetary transfers: The regular case," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1373-1395, July.
    7. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-1385, November.
    8. Olszewski, Wojciech, 2004. "Informal communication," Journal of Economic Theory, Elsevier, vol. 117(2), pages 180-200, August.
    9. Krishna, Vijay & Morgan, John, 2004. "The art of conversation: eliciting information from experts through multi-stage communication," Journal of Economic Theory, Elsevier, vol. 117(2), pages 147-179, August.
    10. Kartik, Navin & Ottaviani, Marco & Squintani, Francesco, 2007. "Credulity, lies, and costly talk," Journal of Economic Theory, Elsevier, vol. 134(1), pages 93-116, May.
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    More about this item

    Keywords

    communication; information transmission; cheap talk; noise;

    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
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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