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A detail-free mediator

  • Vida, Péter
  • Āzacis, Helmuts

We present a cheap talk extension to any two-player, finite, complete information game, and ask what correlations over actions are implementable in Nash equilibria of the extended game. In the extension, players communicate repeatedly through a detail-free mediator that has been studied in Lehrer (1991) and in Gossner and Vieille (2001). The extension captures situations in which people can observe the opponentʼs face during the conversation. While Gossner and Vieille (2001) prove that no correlation can be securely implemented by using only this mediator, we prove a result closer to Lehrer (1991), namely, that the Nash equilibrium payoffs of the extended game essentially coincide with the correlated equilibrium payoffs of the underlying game. The contrasting results can be explained with our additional assumptions that the players can also communicate directly and, more importantly, the private messages sent to the mediator can be recorded and revealed later in the conversation.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 81 (2013)
Issue (Month): C ()
Pages: 101-115

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Handle: RePEc:eee:gamebe:v:81:y:2013:i:c:p:101-115
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
  2. Ehud Lehrer, 1988. "Internal Correlation in Repeated Games," Discussion Papers 800, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Amparo Urbano & Jose Vila, 2004. "Computationally restricted unmediated talk under incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(2), pages 283-320, January.
  4. R. Vijay Krishna, 2004. "Communication in Games of Incomplete Information: The Two-player Case," ESE Discussion Papers 125, Edinburgh School of Economics, University of Edinburgh.
  5. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
  6. 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.
  7. Ben-Porath, Elchanan, 2003. "Cheap talk in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 108(1), pages 45-71, January.
  8. Heller, Yuval, 2005. "A minority-proof cheap-talk protocol," MPRA Paper 7716, University Library of Munich, Germany, revised 26 Feb 2008.
  9. Forges, Françoise & Vida, Péter, 2013. "Implementation of communication equilibria by correlated cheap talk: The two-player case," Theoretical Economics, Econometric Society, vol. 8(1), January.
  10. Amparo Urbano & Jose E. Vila, 2002. "Computational Complexity and Communication: Coordination in Two-Player Games," Econometrica, Econometric Society, vol. 70(5), pages 1893-1927, September.
  11. Ben-Porath, Elchanan, 1998. "Correlation without Mediation: Expanding the Set of Equilibrium Outcomes by "Cheap" Pre-play Procedures," Journal of Economic Theory, Elsevier, vol. 80(1), pages 108-122, May.
  12. Dino Gerardi, 2002. "Unmediated Communication in Games with Complete and Incomplete Information," Cowles Foundation Discussion Papers 1371, Cowles Foundation for Research in Economics, Yale University.
  13. repec:dau:papers:123456789/6031 is not listed on IDEAS
  14. Jarque, Xavier & Ponsati, Clara & Sakovics, Jozsef, 2003. "Mediation: incomplete information bargaining with filtered communication," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 803-830, September.
  15. Cavaliere, Alberto, 2001. " Coordination and the Provision of Discrete Public Goods by Correlated Equilibria," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(3), pages 235-55.
  16. GOSSNER, Olivier, 1997. "Secure protocols or how communication generates correlation," CORE Discussion Papers 1997092, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  17. repec:dau:papers:123456789/6244 is not listed on IDEAS
  18. Vanessa Teague, 2008. "Problems With Coordination in Two-Player Games: Comment on "Computational Complexity and Communication"," Econometrica, Econometric Society, vol. 76(6), pages 1559-1564, November.
  19. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
  20. Ehud Lehrer & Sylvain Sorin, 1994. "One-Shot Public Mediated Talk," Discussion Papers 1108, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  21. Forges, F., 1987. "Universal mechanisms," CORE Discussion Papers 1987004, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  22. Lehrer, Ehud, 1996. "Mediated Talk," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 177-88.
  23. Olivier Gossner & Nicolas Vieille, 2001. "Repeated communication through the mechanism," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 41-60.
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