IDEAS home Printed from https://ideas.repec.org/p/bie/wpaper/420.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://pub.uni-bielefeld.de/download/2316258/2319858
    File Function: First Version, 2008
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Yaron Azrieli & Ehud Lehrer, 2004. "Categorization generated by prototypes -- an axiomatic approach," Game Theory and Information 0405003, University Library of Munich, Germany.
    3. 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.
    4. Oechssler, Jorg & Riedel, Frank, 2002. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Journal of Economic Theory, Elsevier, vol. 107(2), pages 223-252, December.
    5. Robson, A.J., 1989. "Efficiency In Evolutionary Games: Darwin, Nash And Secret Handshake," Papers 89-22, Michigan - Center for Research on Economic & Social Theory.
    6. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    7. 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.
    8. Warneryd Karl, 1993. "Cheap Talk, Coordination, and Evolutionary Stability," Games and Economic Behavior, Elsevier, vol. 5(4), pages 532-546, October.
    9. Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2009. "Brown-von Neumann-Nash dynamics: The continuous strategy case," Games and Economic Behavior, Elsevier, vol. 65(2), pages 406-429, March.
    10. Matsui, Akihiko, 1991. "Cheap-talk and cooperation in a society," Journal of Economic Theory, Elsevier, vol. 54(2), pages 245-258, August.
    11. 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.
    12. Azrieli, Yaron, 2009. "Characterization of multidimensional spatial models of elections with a valence dimension," MPRA Paper 14513, University Library of Munich, Germany.
    13. Sobel, Joel, 1993. "Evolutionary stability and efficiency," Economics Letters, Elsevier, vol. 42(2-3), pages 301-312.
    14. Crawford, Vincent P & Sobel, Joel, 1982. "Strategic Information Transmission," Econometrica, Econometric Society, vol. 50(6), pages 1431-1451, November.
    15. K. Schlag, 2010. "Cheap Talk and Evolutionary Dynamics," Levine's Working Paper Archive 541, David K. Levine.
    16. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, Oxford University Press, vol. 87(3), pages 355-374.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Foerster, Manuel, 2018. "Finite languages, persuasion bias, and opinion fluctuations," Journal of Economic Behavior & Organization, Elsevier, vol. 149(C), pages 46-57.
    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 Sep 2022.
    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. Toru Suzuki, 2021. "Pragmatic Ambiguity and Rational Miscommunication," Working Paper Series 2021/04, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    12. 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.
    13. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
    14. 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.
    15. Stéphan Sémirat, 2019. "Strategic information transmission despite conflict," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(3), pages 921-956, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jäger, Gerhard & Metzger, Lars P. & Riedel, Frank, 2011. "Voronoi languages," Games and Economic Behavior, Elsevier, vol. 73(2), pages 517-537.
    2. Förster, Manuel & Riedel, Frank, 2016. "Distorted Voronoi languages," Center for Mathematical Economics Working Papers 458, Center for Mathematical Economics, Bielefeld University.
    3. Brian Skyrms, 2003. "Signals, Evolution and the Explanatory Power of Transient Information," Levine's Working Paper Archive 618897000000000799, David K. Levine.
    4. Paola Manzini & Abdolkarim Sadrieh & Nicolaas J. Vriend, 2009. "On Smiles, Winks and Handshakes as Coordination Devices," Economic Journal, Royal Economic Society, vol. 119(537), pages 826-854, April.
    5. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    6. Stefano Demichelis & Jorgen W. Weibull, 2008. "Language, Meaning, and Games: A Model of Communication, Coordination, and Evolution," American Economic Review, American Economic Association, vol. 98(4), pages 1292-1311, September.
    7. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    8. Herold, Florian & Kuzmics, Christoph, 2020. "The evolution of taking roles," Journal of Economic Behavior & Organization, Elsevier, vol. 174(C), pages 38-63.
    9. Yuval Heller & Christoph Kuzmics, 2019. "Renegotiation and Coordination with Private Values," Graz Economics Papers 2019-10, University of Graz, Department of Economics.
    10. Banerjee, Abhijit & Weibull, Jorgen W., 2000. "Neutrally Stable Outcomes in Cheap-Talk Coordination Games," Games and Economic Behavior, Elsevier, vol. 32(1), pages 1-24, July.
    11. Heller, Yuval & Mohlin, Erik, 2019. "Coevolution of deception and preferences: Darwin and Nash meet Machiavelli," Games and Economic Behavior, Elsevier, vol. 113(C), pages 223-247.
    12. Robert J. Aumann & Sergiu Hart, 2003. "Long Cheap Talk," Econometrica, Econometric Society, vol. 71(6), pages 1619-1660, November.
      • Robert J. Aumann & Sergiu Hart, 2002. "Long Cheap Talk," Discussion Paper Series dp284, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem, revised Nov 2002.
    13. Yuval Heller & Christoph Kuzmics, 2020. "Communication, Renegotiation and Coordination with Private Values," Papers 2005.05713, arXiv.org, revised Nov 2023.
    14. Norman, Thomas W.L., 2008. "Dynamically stable sets in infinite strategy spaces," Games and Economic Behavior, Elsevier, vol. 62(2), pages 610-627, March.
    15. Chen, Ying, 2011. "Perturbed communication games with honest senders and naive receivers," Journal of Economic Theory, Elsevier, vol. 146(2), pages 401-424, March.
    16. Heller, Yuval & Kuzmics, Christoph, 2020. "Communication, Renegotiation and Coordination with Private Values (Extended Version)," MPRA Paper 102926, University Library of Munich, Germany, revised 26 Jul 2021.
    17. Jason McKenzie Alexander & Brian Skyrms & Sandy Zabell, 2012. "Inventing New Signals," Dynamic Games and Applications, Springer, vol. 2(1), pages 129-145, March.
    18. de Groot Ruiz, Adrian & Offerman, Theo & Onderstal, Sander, 2015. "Equilibrium selection in experimental cheap talk games," Games and Economic Behavior, Elsevier, vol. 91(C), pages 14-25.
    19. Sendhil Mullainathan & Joshua Schwartzstein & Andrei Shleifer, 2008. "Coarse Thinking and Persuasion," The Quarterly Journal of Economics, Oxford University Press, vol. 123(2), pages 577-619.
    20. Paola Manzini & Abdolkarim Sadrieh & Nicolaas J. Vriend, 2009. "On Smiles, Winks and Handshakes as Coordination Devices," Economic Journal, Royal Economic Society, vol. 119(537), pages 826-854, April.

    More about this item

    Keywords

    Communication game; Dynamic stability; Cheap talk; Voronoi tesselation; Signaling game;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:420. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bettina Weingarten (email available below). General contact details of provider: https://edirc.repec.org/data/imbiede.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.