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Noisy Talk

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  • Andreas Blume
  • Oliver Board
  • Kohei Kawamura

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 e ? (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.

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Bibliographic Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 167.

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Length: 53
Date of creation: 20 Aug 2007
Date of revision:
Handle: RePEc:edn:esedps:167

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Related research

Keywords: Communication; information transmission; cheap talk; noise.;

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References

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  1. 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.
  2. F. Forges, 2010. "An Approach to Communication Equilibrium," Levine's Working Paper Archive 516, David K. Levine.
  3. Robert J. Aumann & Sergiu Hart, 2003. "Long Cheap Talk," Econometrica, Econometric Society, vol. 71(6), pages 1619-1660, November.
  4. 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.
  5. Olszewski, Wojciech, 2004. "Informal communication," Journal of Economic Theory, Elsevier, vol. 117(2), pages 180-200, August.
  6. Navin Kartik, 2005. "Information Transmission with Cheap and Almost-Cheap Talk," NajEcon Working Paper Reviews 666156000000000650, www.najecon.org.
  7. 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.
  8. 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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