IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v81y2013icp101-115.html
   My bibliography  Save this article

A detail-free mediator

Author

Listed:
  • Vida, Péter
  • Āzacis, Helmuts

Abstract

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.

Suggested Citation

  • Vida, Péter & Āzacis, Helmuts, 2013. "A detail-free mediator," Games and Economic Behavior, Elsevier, vol. 81(C), pages 101-115.
    • Handle: RePEc:eee:gamebe:v:81:y:2013:i:c:p:101-115
    DOI: 10.1016/j.geb.2013.04.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825613000699
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2013.04.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. repec:dau:papers:123456789/8159 is not listed on IDEAS
    2. Imre Bárány, 1992. "Fair Distribution Protocols or How the Players Replace Fortune," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 327-340, May.
    3. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    4. repec:dau:papers:123456789/6244 is not listed on IDEAS
    5. Heller, Yuval, 2010. "Minority-proof cheap-talk protocol," Games and Economic Behavior, Elsevier, vol. 69(2), pages 394-400, July.
    6. Lehrer, Ehud, 1996. "Mediated Talk," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 177-188.
    7. Forges, Francoise, 1990. "Universal Mechanisms," Econometrica, Econometric Society, vol. 58(6), pages 1341-1364, November.
    8. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    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 235-255.
    10. , & ,, 2013. "Implementation of communication equilibria by correlated cheap talk: The two-player case," Theoretical Economics, Econometric Society, vol. 8(1), January.
    11. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 431-456.
    12. R. Vijay Krishna, 2004. "Communication in Games of Incomplete Information: The Two-player Case," Edinburgh School of Economics Discussion Paper Series 125, Edinburgh School of Economics, University of Edinburgh.
    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. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 69-89, November.
    16. GOSSNER , Olivier & VIEILLE, Nicolas, 1998. "Repeated communication through the mechanism “and”," LIDAM Discussion Papers CORE 1998056, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. 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.
    18. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Ben-Porath, Elchanan, 2003. "Cheap talk in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 108(1), pages 45-71, January.
    24. 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.
    25. Gerardi, Dino, 2004. "Unmediated communication in games with complete and incomplete information," Journal of Economic Theory, Elsevier, vol. 114(1), pages 104-131, January.
    26. Lehrer, Ehud & Sorin, Sylvain, 1997. "One-Shot Public Mediated Talk," Games and Economic Behavior, Elsevier, vol. 20(2), pages 131-148, August.
    27. Alberto Cavaliere, 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 235-255, July.
    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. , & ,, 2013. "Implementation of communication equilibria by correlated cheap talk: The two-player case," Theoretical Economics, Econometric Society, vol. 8(1), January.
    2. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.
    3. Goltsman, Maria & Pavlov, Gregory, 2014. "Communication in Cournot oligopoly," Journal of Economic Theory, Elsevier, vol. 153(C), pages 152-176.

    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. Peter Vida, 2005. "A Detail-free Mediator and the 3 Player Case," CERS-IE WORKING PAPERS 0511, Institute of Economics, Centre for Economic and Regional Studies.
    2. Kar, Anirban & Ray, Indrajit & Serrano, Roberto, 2010. "A difficulty in implementing correlated equilibrium distributions," Games and Economic Behavior, Elsevier, vol. 69(1), pages 189-193, May.
    3. Kar, Anirban & Ray, Indrajit & Serrano, Roberto, 2005. "Multiple equilibria as a difficulty in understanding correlated distributions," UC3M Working papers. Economics we057238, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Indrajit Ray, 2002. "Multiple Equilibrium Problem and Non-Canonical Correlation Devices," Working Papers 2002-24, Brown University, Department of Economics.
    5. Heng Liu, 2017. "Correlation and unmediated cheap talk in repeated games with imperfect monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1037-1069, November.
    6. , & ,, 2013. "Implementation of communication equilibria by correlated cheap talk: The two-player case," Theoretical Economics, Econometric Society, vol. 8(1), January.
    7. Heller, Yuval, 2010. "Minority-proof cheap-talk protocol," Games and Economic Behavior, Elsevier, vol. 69(2), pages 394-400, July.
    8. Gerardi, Dino, 2004. "Unmediated communication in games with complete and incomplete information," Journal of Economic Theory, Elsevier, vol. 114(1), pages 104-131, January.
    9. Heller, Yuval & Solan, Eilon & Tomala, Tristan, 2012. "Communication, correlation and cheap-talk in games with public information," Games and Economic Behavior, Elsevier, vol. 74(1), pages 222-234.
    10. Gerardi, Dino & Myerson, Roger B., 2007. "Sequential equilibria in Bayesian games with communication," Games and Economic Behavior, Elsevier, vol. 60(1), pages 104-134, July.
    11. Kalai, Adam Tauman & Kalai, Ehud & Lehrer, Ehud & Samet, Dov, 2010. "A commitment folk theorem," Games and Economic Behavior, Elsevier, vol. 69(1), pages 127-137, May.
    12. repec:dau:papers:123456789/5279 is not listed on IDEAS
    13. repec:dau:papers:123456789/8159 is not listed on IDEAS
    14. Renault, Jerome & Tomala, Tristan, 2004. "Learning the state of nature in repeated games with incomplete information and signals," Games and Economic Behavior, Elsevier, vol. 47(1), pages 124-156, April.
    15. Goltsman, Maria & Pavlov, Gregory, 2014. "Communication in Cournot oligopoly," Journal of Economic Theory, Elsevier, vol. 153(C), pages 152-176.
    16. 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.
    17. Gossner, Olivier, 1998. "Secure Protocols or How Communication Generates Correlation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 69-89, November.
    18. Forges, Francoise & Koessler, Frederic, 2005. "Communication equilibria with partially verifiable types," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 793-811, November.
    19. R. Vijay Krishna, 2004. "Communication in Games of Incomplete Information: The Two-player Case," Edinburgh School of Economics Discussion Paper Series 125, Edinburgh School of Economics, University of Edinburgh.
    20. Urbano, A. & Vila, J. E., 2004. "Unmediated communication in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 46(1), pages 143-173, January.
    21. Izmalkov, Sergei & Lepinski, Matt & Micali, Silvio, 2011. "Perfect implementation," Games and Economic Behavior, Elsevier, vol. 71(1), pages 121-140, January.
    22. Vijay Krishna, R., 2007. "Communication in games of incomplete information: Two players," Journal of Economic Theory, Elsevier, vol. 132(1), pages 584-592, January.

    More about this item

    Keywords

    Correlated equilibrium; Detail-free mechanism; Mediated pre-play communication;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:eee:gamebe:v:81:y:2013:i:c:p:101-115. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.