Voronoi languages: Equilibria in cheap-talk games with high-dimensional types and few signals

doi:10.1016/j.geb.2011.03.008

Games and Economic Behavior

Volume 73, Issue 2, November 2011, Pages 517-537

https://doi.org/10.1016/j.geb.2011.03.008 Get rights and content

Abstract

We study a communication game of common interest in which the sender observes one of infinite types and sends one of finite messages which is interpreted by the receiver. In equilibrium there is no full separation but types are clustered into contiguous cells. We give a full characterization of the strict Nash equilibria of this game as Voronoi languages. As the strategy set is infinite static stability concepts for finite games such as ESS are no longer sufficient for Lyapunov stability in the replicator dynamics. We give examples of unstable strict Nash equilibria and stable inefficient Voronoi languages. We derive efficient Voronoi languages with a large number of words and numerically illustrate stability of some Voronoi languages with large message spaces and non-uniformly distributed types.

Highlights

► We study a communication game with infinite types and finite messages. ► Strict Nash equilibria of this game are Voronoi languages and vice versa. ► There are strict but unstable and stable but inefficient Nash equilibria. ► We illustrate stability of some languages with non-uniform types and many messages.

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^☆: We would like to thank Joseph Hofbauer from University of Vienna and the audiences of the North American Summer Meeting of the Econometric Society in Boston, 2009, the annual meeting of the German Economic Association in Magdeburg, 2009, and the economic seminars at TU Dortmund and Max-Planck-Institute for Economics, Jena, for their comments. The feedback that we received from the audience of the workshop “Game Theory and Communication: Prospects and Syntheses” at Stanford University, especially Chris Pottʼs detailed commentary, were also very helpful. The research that led to this paper has been supported by project A6 of the CRC 673 “Alignment in Communication” and by the International Research Training Group EBIM (“Economic Behavior and Interaction Models”), both of the German Research Foundation, DFG, which is gratefully acknowledged.

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Voronoi languages: Equilibria in cheap-talk games with high-dimensional types and few signals☆

Abstract

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