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Signaling and mediation in games with common interests

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  • Lehrer, Ehud
  • Rosenberg, Dinah
  • Shmaya, Eran
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    Abstract

    Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential stochastic signals that depend on the actual state of nature. These signals provide the players with partial information about the state of nature and may also serve as a means of correlation. Different information structures induce different outcomes. An information structure is better than another, with respect to a certain solution concept, if the highest solution payoff it induces is at least that induced by the other structure. This paper characterizes the situation where one information structure is better than another with respect to various solution concepts: Nash equilibrium, strategic-normal-form correlated equilibrium, agent-normal-form correlated equilibrium and belief-invariant Bayesian solution. These solution concepts differ from one another in the scope of communication allowed between the players. The characterizations use maps that stochastically translate signals of one structure to signals of another.

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    Bibliographic Info

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

    Volume (Year): 68 (2010)
    Issue (Month): 2 (March)
    Pages: 670-682

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    Handle: RePEc:eee:gamebe:v:68:y:2010:i:2:p:670-682

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    Web page: http://www.elsevier.com/locate/inca/622836

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    References

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    1. Bruno Bassan & Olivier Gossner & Marco Scarsini & Shmuel Zamir, 2001. "Positive value of information in games," Discussion Paper Series dp294, The Center for the Study of Rationality, Hebrew University, Jerusalem, revised Jul 2002.
    2. Jeffrey C. Ely & Marcin Peski, . "Hierarchies Of Belief And Interim Rationalizability," Discussion Papers 1388, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. F. Forges, 2010. "An Approach to Communication Equilibrium," Levine's Working Paper Archive 516, David K. Levine.
    4. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.
    5. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    6. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
    7. Neyman, Abraham, 1991. "The positive value of information," Games and Economic Behavior, Elsevier, vol. 3(3), pages 350-355, August.
    8. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
    9. Hirshleifer, Jack, 1971. "The Private and Social Value of Information and the Reward to Inventive Activity," American Economic Review, American Economic Association, vol. 61(4), pages 561-74, September.
    10. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," CORE Discussion Papers 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:
    1. Heller, Yuval & Winter, Eyal, 2013. "Rule Rationality," MPRA Paper 48746, University Library of Munich, Germany.
    2. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    3. Igal Milchtaich, 2014. "Implementability of correlated and communication equilibrium outcomes in incomplete information games," International Journal of Game Theory, Springer, vol. 43(2), pages 283-350, May.

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