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

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Author Info

  • Gerhard Jäger

    (Tübingen University)

  • Lars Koch-Metzger

    (Institute of Mathematical Economics, Bielefeld University)

  • Frank Riedel

    ()
    (Institute of Mathematical Economics, Bielefeld University)

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 convex categories. We give a full characterization of the strict Nash equilibria of this game by representing these categories by 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 categories and numerically illustrate stability of some Voronoi languages with large message spaces and non-uniformly distributed types.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-420.pdf
File Function: First version, 2009
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 420.

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Length: 53 pages
Date of creation: Aug 2009
Date of revision:
Handle: RePEc:bie:wpaper:420

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Related research

Keywords: Cheap Talk; Signaling Game; Communication Game; Dynamic stability; Voronoi tesselation;

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References

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  1. Blume Andreas & Kim Yong-Gwan & Sobel Joel, 1993. "Evolutionary Stability in Games of Communication," Games and Economic Behavior, Elsevier, vol. 5(4), pages 547-575, October.
  2. Fryer Roland & Jackson Matthew O., 2008. "A Categorical Model of Cognition and Biased Decision Making," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-44, February.
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  4. Joerg Oechssler & Frank Riedel, 1998. "Evolutionary Dynamics on Infinite Strategy Spaces," Game Theory and Information 9805002, EconWPA, revised 12 May 1998.
  5. Azrieli, Yaron, 2009. "Characterization of multidimensional spatial models of elections with a valence dimension," MPRA Paper 14513, University Library of Munich, Germany.
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  8. Josef Hofbauer & Joerg Oechssler & Frank Riedel, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Game Theory and Information 0512003, EconWPA.
  9. Heifetz, Aviad & Shannon, Chris & Spiegel, Yossi, 2007. "What to maximize if you must," Journal of Economic Theory, Elsevier, vol. 133(1), pages 31-57, March.
  10. Spence, A Michael, 1973. "Job Market Signaling," The Quarterly Journal of Economics, MIT Press, vol. 87(3), pages 355-74, August.
  11. Warneryd Karl, 1993. "Cheap Talk, Coordination, and Evolutionary Stability," Games and Economic Behavior, Elsevier, vol. 5(4), pages 532-546, October.
  12. V. Crawford & J. Sobel, 2010. "Strategic Information Transmission," Levine's Working Paper Archive 544, David K. Levine.
  13. Ross Cressman & Josef Hofbauer & Frank Riedel, 2005. "Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space," Bonn Econ Discussion Papers bgse12_2005, University of Bonn, Germany.
  14. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August.
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  18. Yaron Azrieli & Ehud Lehrer, 2004. "Categorization generated by prototypes -- an axiomatic approach," Game Theory and Information 0405003, EconWPA.
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Citations

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Cited by:
  1. Hertel, Johanna & Smith, John, 2011. "Not so cheap talk: Costly and discrete communication," MPRA Paper 29148, University Library of Munich, Germany.
  2. K.J.M. De Jaegher & R. van Rooij, 2011. "Game-theoretic pragmatics under conflicting and common interests," Working Papers 11-25, Utrecht School of Economics.
  3. Penélope Hernández & Bernhard von Stengel, 2012. "Nash Codes for Noisy Channels," Discussion Papers in Economic Behaviour 0912, University of Valencia, ERI-CES.
  4. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.

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