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A Detail-free Mediator and the 3 Player Case

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Author Info

  • Peter Vida

    ()
    (Universitat Autonoma de Barcelona, IDEA)

Abstract

Two players can make use of a trusted third party who mediates and partially resolves their conflict. Usually, the mediator should be aware of the situation and give suggestions to the players accordingly. However, a corrupt mediator can have a big influence on the outcome of the game. We single out a transparent mediator which can be safely applied in any two player game without loss of efficiency. That is, the mediator is independent of the game and the desired outcome. Technically, we show that any correlated equilibrium of any two player game can be obtained as Nash equilibria of the game, extended with cheap, pre-play communication, where players can communicate through the proposed mediator. The key idea is that after the mediated communication the players can have a plain conversation. In particular, the mediating communication device is transparent, controllable and is the same for all games and for all equilibrium distributions. We extend the result to three player games and show that one of the players can play the role of the mediator. We implement the set of correlated equilibrium in Nash equilibria of an extended game where the players have a plain conversation. The central assumption is that players can be invited to eavesdrop a private conversation. We extend the analysis to games with incomplete information and to the set of communication equilibria.

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File URL: http://econ.core.hu/doc/dp/dp/mtdp0511.pdf
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Bibliographic Info

Paper provided by Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences in its series IEHAS Discussion Papers with number 0511.

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Length: 43 pages
Date of creation: Oct 2005
Date of revision:
Handle: RePEc:has:discpr:0511

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Related research

Keywords: cheap talk; communication device; correlated equilibrium; communi- cation equilibrium; detail-free mechanism; mediator;

References

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  1. Aumann, Robert J. & Heifetz, Aviad, 2001. "Incomplete Information," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1124, California Institute of Technology, Division of the Humanities and Social Sciences.
  2. Forges, F., 1984. "An approach to communication equilibria," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1984035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. FORGES, Françoise, . "Universal mechanisms," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -914, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Amparo Urbano & Jose Vila, 2004. "Computationally restricted unmediated talk under incomplete information," Economic Theory, Springer, Springer, vol. 23(2), pages 283-320, January.
  5. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. GOSSNER, Olivier, 1997. "Secure protocols or how communication generates correlation," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1997092, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. V. Crawford & J. Sobel, 2010. "Strategic Information Transmission," Levine's Working Paper Archive 544, David K. Levine.
  8. Amparo Urbano & Jose E. Vila, 2002. "Computational Complexity and Communication: Coordination in Two-Player Games," Econometrica, Econometric Society, Econometric Society, vol. 70(5), pages 1893-1927, September.
  9. 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.
  10. Farrell, Joseph, 1988. "Communication, coordination and Nash equilibrium," Economics Letters, Elsevier, Elsevier, vol. 27(3), pages 209-214.
  11. Kay Mitusch & Roland Strausz, . "Mediators and Mechanism Design: Why Firms Hire Consultants," Papers, Departmental Working Papers 005, Departmental Working Papers.
  12. Joseph Farrell & Matthew Rabin, 1996. "Cheap Talk," Journal of Economic Perspectives, American Economic Association, American Economic Association, vol. 10(3), pages 103-118, Summer.
  13. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer, Springer, vol. 19(4), pages 431-56.
  14. Olivier Gossner & Nicolas Vieille, 2001. "Repeated communication through the mechanism," International Journal of Game Theory, Springer, Springer, vol. 30(1), pages 41-60.
  15. Robert J. Aumann & Sergiu Hart, 2003. "Long Cheap Talk," Econometrica, Econometric Society, Econometric Society, vol. 71(6), pages 1619-1660, November.
  16. Ben-Porath, Elchanan, 2003. "Cheap talk in games with incomplete information," Journal of Economic Theory, Elsevier, Elsevier, vol. 108(1), pages 45-71, January.
  17. Lehrer, Ehud, 1996. "Mediated Talk," International Journal of Game Theory, Springer, Springer, vol. 25(2), pages 177-88.
  18. Myerson, Roger B., 1982. "Optimal coordination mechanisms in generalized principal-agent problems," Journal of Mathematical Economics, Elsevier, vol. 10(1), pages 67-81, June.
  19. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Economics Papers from University Paris Dauphine 123456789/6244, Paris Dauphine University.
  20. Lehrer, Ehud & Sorin, Sylvain, 1997. "One-Shot Public Mediated Talk," Games and Economic Behavior, Elsevier, Elsevier, vol. 20(2), pages 131-148, August.
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  22. Gossner, Olivier & Vieille, Nicolas, 2001. "Repeated Communication Through the Mechanism And," Economics Papers from University Paris Dauphine 123456789/6031, Paris Dauphine University.
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Cited by:
  1. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, Springer, vol. 61(4), pages 329-344, December.

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