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Subjective games and equilibria

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  • Kalai, Ehud
  • Lehrer, Ehud
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    Abstract

    Applying the concepts of Nash, Bayesian, and correlated equilibria to the analysis of strategic interaction requires that players possess objective knowledge of the game and opponents' strategies. Such knowledge is often not available. The proposed notions of subjective games and of subjective Nash and correlated equilibria replace essential but unavailable objective knowledge by subjective assessments. When playing a subjective game repeatedly, subjective optimizers converge to a subjective equilibrium. We apply this approach to some well known examples including single- and multi-person, multi-arm bandit games and repeated Cournot oligopoly games. Journal of Economic Literature Classification Numbers: C73 and C83.

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    Bibliographic Info

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

    Volume (Year): 8 (1995)
    Issue (Month): 1 ()
    Pages: 123-163

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    Handle: RePEc:eee:gamebe:v:8:y:1995:i:1:p:123-163

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

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    1. Ariel Rubinstein & Asher Wolinsky, 1991. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Discussion Papers 933, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. von Hayek, Friedrich August, 1989. "The Pretence of Knowledge," American Economic Review, American Economic Association, vol. 79(6), pages 3-7, December.
    3. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
    4. Gilboa, Itzhak & Schmeidler, David, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, MIT Press, vol. 110(3), pages 605-39, August.
    5. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
    6. Schmidt,Klaus M., 1991. "Reputation and equilibrium characterization in repeated games of conflicting interests," Discussion Paper Serie A 333, University of Bonn, Germany.
    7. Green, Edward J. & Porter, Robert H., 1982. "Noncooperative Collusion Under Imperfect Price Information," Working Papers 367, California Institute of Technology, Division of the Humanities and Social Sciences.
    8. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer, vol. 19(4), pages 431-56.
    9. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
    10. Porter, Robert H., 1983. "Optimal cartel trigger price strategies," Journal of Economic Theory, Elsevier, vol. 29(2), pages 313-338, April.
    11. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
    13. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    14. Ehud Kalai & Ehud Lehrer, 1992. "Weak and Strong Merging of Opinions," Discussion Papers 983, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    15. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    16. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
    17. Dilip Abreu & David G. Pearce & Ennio Stacchetti, 1986. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Cowles Foundation Discussion Papers 791, Cowles Foundation for Research in Economics, Yale University.
    18. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-40, September.
    19. Crawford, Vincent P & Haller, Hans, 1990. "Learning How to Cooperate: Optimal Play in Repeated Coordination Games," Econometrica, Econometric Society, vol. 58(3), pages 571-95, May.
    20. Sylvain SORIN, 1992. "Information and Rationality : Some Comments," Annales d'Economie et de Statistique, ENSAE, issue 25-26, pages 315-325.
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