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

Author

Listed:
  • Jäger, Gerhard

    (Center for Mathematical Economics, Bielefeld University)

  • Koch-Metzger, Lars

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for 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.

Suggested Citation

  • Jäger, Gerhard & Koch-Metzger, Lars & Riedel, Frank, 2011. "Voronoi languages. Equilibria in cheap-talk games with high-dimensional types and few signals," Center for Mathematical Economics Working Papers 420, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:420
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    File URL: https://pub.uni-bielefeld.de/download/2316258/2319858
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    References listed on IDEAS

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    Cited by:

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    2. Penélope Hernández & Bernhard von Stengel, 2014. "Nash Codes for Noisy Channels," Operations Research, INFORMS, vol. 62(6), pages 1221-1235, December.
    3. Yunus C. Aybas & Eray Turkel, 2019. "Persuasion with Coarse Communication," Papers 1910.13547, arXiv.org, revised May 2024.
    4. Sémirat, S., 2016. "Vertical conflict of interest and horizontal inequities," Working Papers 2016-06, Grenoble Applied Economics Laboratory (GAEL).
    5. Johanna Hertel & John Smith, 2013. "Not so cheap talk: costly and discrete communication," Theory and Decision, Springer, vol. 75(2), pages 267-291, August.
    6. Hernández, Penélope & Urbano, Amparo & Vila, José E., 2012. "Pragmatic languages with universal grammars," Games and Economic Behavior, Elsevier, vol. 76(2), pages 738-752.
    7. Gerrit Bauch, 2023. "Underreaction and dynamic inconsistency in communication games under noise," Papers 2311.12496, arXiv.org.
    8. Suzuki, Toru, 2023. "Endogenous ambiguity and rational miscommunication," Journal of Economic Theory, Elsevier, vol. 211(C).
    9. Bauch, Gerrit, 2021. "Effects of Noise on the Grammar of Languages," Center for Mathematical Economics Working Papers 655, Center for Mathematical Economics, Bielefeld University.
    10. Anqi Li & Ming Yang, 2018. "Optimal Incentive Contract with Endogenous Monitoring Technology," Papers 1810.11471, arXiv.org, revised Nov 2019.
    11. Dilmé, Francesc, 2023. "Communication between unbiased agents," Games and Economic Behavior, Elsevier, vol. 142(C), pages 613-622.
    12. Toru Suzuki, 2021. "Pragmatic Ambiguity and Rational Miscommunication," Working Paper Series 2021/04, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    13. Blume, Andreas & Noussair, Charles N. & Ye, Bohan, 2024. "Fragile meaning - an experiment," Journal of Economic Theory, Elsevier, vol. 216(C).
    14. Blume, Andreas, 2018. "Failure of common knowledge of language in common-interest communication games," Games and Economic Behavior, Elsevier, vol. 109(C), pages 132-155.
    15. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
    16. 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.
    17. Stéphan Sémirat, 2019. "Strategic information transmission despite conflict," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 921-956, September.
    18. Avi Lichtig & Helene Mass, 2024. "Optimal Testing in Disclosure Games," CRC TR 224 Discussion Paper Series crctr224_2024_543, University of Bonn and University of Mannheim, Germany.

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    Keywords

    Communication game; Dynamic stability; Cheap talk; Voronoi tesselation; Signaling game;
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