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

  • Gerhard Jäger

    (Tübingen University)

  • Lars Koch-Metzger

    (Institute of Mathematical Economics, Bielefeld University)

  • Frank Riedel

    ()

    (Institute of Mathematical Economics, Bielefeld University)

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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Paper provided by Center for Mathematical Economics, Bielefeld University in its series Center for Mathematical Economics 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
Contact details of provider: Postal: Postfach 10 01 31, 33501 Bielefeld
Phone: +49(0)521-106-4907
Web page: http://www.imw.uni-bielefeld.de/

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