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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Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number
167.
Board, Oliver J. & Blume, Andreas & Kawamura, Kohei, 2007.
"Noisy talk,"
Theoretical Economics,
Society for Economic Theory, vol. 2(4), pages 395-440, December.
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Find related papers by JEL classification: C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Robert J. Aumann & Sergiu Hart, 2003.
"Long Cheap Talk,"
Econometrica,
Econometric Society, vol. 71(6), pages 1619-1660, November.
[Downloadable!] (restricted)
Other versions:
Robert J. Aumann & Sergiu Hart, 2002.
"Long Cheap Talk,"
Discussion Paper Series
dp284, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem, revised Nov 2002.
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Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)
Oliver Board & Andreas Blume, 2008.
"Intentional Vagueness,"
Working Papers
365, University of Pittsburgh, Department of Economics, revised Aug 2008.
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Other versions:
Andreas Blume & Oliver Board, 2009.
"Intentional Vagueness,"
Working Papers
381, University of Pittsburgh, Department of Economics, revised May 2009.
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