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Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability

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  • A. Rubinstein
  • A. Wolinsky

Abstract

For a steady state to be a Nash equilibrium the agents have to perfectly observe the actions of others. This paper suggests a solution concept for cases where players observe only an imperfect signal of what the others' actions are. The model is enriched by specifying the signal that each player has about the actions taken by the others. The solution, which we call rationalizbale conjectural equilibrium (RCE), is a profile of actions such that each player's action is optimal, given the assumption that it is common knowledge that all players maximize their expected utility given their knowledge. The RCE occupies an intermediary position between Nash equilibrium on one hand and Rationalizability style Bernheim-Pearce on the other hand. The concept is demonstrated by several examples in which it refines the rationalizability concept and still is not equivalent to Nash equilibrium.
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  • A. Rubinstein & A. Wolinsky, 2010. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Levine's Working Paper Archive 369, David K. Levine.
  • Handle: RePEc:cla:levarc:369
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    References listed on IDEAS

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    1. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    2. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
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    Cited by:

    1. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 1999. "Payoff Information and Self-Confirming Equilibrium," Journal of Economic Theory, Elsevier, vol. 89(2), pages 165-185, December.
    2. Gilli, Mario, 1999. "On Non-Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 27(2), pages 184-203, May.
    3. Drew Fudenberg & David K. Levine, 2006. "Superstition and Rational Learning," American Economic Review, American Economic Association, vol. 96(3), pages 630-651, June.
    4. Desgranges, Gabriel & Gauthier, Stéphane, 2016. "Rationalizability and efficiency in an asymmetric Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 44(C), pages 163-176.
    5. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    6. Lagunoff, Roger, 1997. "On the dynamic selection of mechanisms for provision of public projects," Journal of Economic Dynamics and Control, Elsevier, vol. 21(10), pages 1699-1725, August.
    7. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 2004. "Learning to play Bayesian games," Games and Economic Behavior, Elsevier, vol. 46(2), pages 282-303, February.
    8. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-573, May.
    9. Joseph Greenberg & Sudheer Gupta & Xiao Luo, 2009. "Mutually acceptable courses of action," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 91-112, July.
    10. Yaron Azrieli, 2009. "On pure conjectural equilibrium with non-manipulable information," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 209-219, June.
    11. S. Nageeb Ali, 2011. "Learning Self-Control," The Quarterly Journal of Economics, Oxford University Press, vol. 126(2), pages 857-893.
    12. Shimoji, Makoto, 2012. "Outcome-equivalence of self-confirming equilibrium and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 75(1), pages 441-447.
    13. Ignacio Esponda & Demian Pouzo, 2014. "Berk-Nash Equilibrium: A Framework for Modeling Agents with Misspecified Models," Papers 1411.1152, arXiv.org, revised May 2016.
    14. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Self-Confirming Equilibrium and Model Uncertainty," American Economic Review, American Economic Association, vol. 105(2), pages 646-677, February.
    15. McBride, Michael, 2008. "Position-specific information in social networks: Are you connected?," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 283-295, September.
    16. Kalai, Ehud & Lehrer, Ehud, 1995. "Subjective games and equilibria," Games and Economic Behavior, Elsevier, vol. 8(1), pages 123-163.
    17. Heller, Yuval, 2012. "Justifiable choice," Games and Economic Behavior, Elsevier, vol. 76(2), pages 375-390.
    18. repec:hal:journl:halshs-00975002 is not listed on IDEAS
    19. József Sákovics, 2001. "Games of Incomplete Information Without Common Knowledge Priors," Theory and Decision, Springer, vol. 50(4), pages 347-366, June.
    20. Azrieli, Yaron, 2007. "Thinking categorically about others: A conjectural equilibrium approach," MPRA Paper 3843, University Library of Munich, Germany.
    21. Astrid Gamba, 2011. "On the Evolution of Preferences," Jena Economic Research Papers 2011-032, Friedrich-Schiller-University Jena.
    22. Pierpaolo Battigalli & Emiliano Catonini & Giacomo Lanzani & Massimo Marinacci, 2017. "Ambiguity Attitudes and Self-Confi rming Equilibrium in Sequential Games," Working Papers 607, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    23. Luo, Xiao & Ma, Chenghu, 2001. "Stable equilibrium in beliefs in extensive games with perfect information," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1801-1825, November.
    24. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.
    25. Azrieli, Yaron, 2009. "Categorizing others in a large game," Games and Economic Behavior, Elsevier, vol. 67(2), pages 351-362, November.

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