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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. Rubinstein Ariel & Wolinsky Asher, 1994. "Rationalizable Conjectural Equilibrium: Between Nash and Rationalizability," Games and Economic Behavior, Elsevier, vol. 6(2), pages 299-311, March.
    2. Itzhak Gilboa & David Schmeidler, 1992. "Case-Based Decision Theory," Discussion Papers 994, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Kalai, Ehud & Lehrer, Ehud, 1991. "Rational Learning Leads to Nash Equilibrium," Working Papers 91-18, C.V. Starr Center for Applied Economics, New York University.
    4. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
    5. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    6. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
    7. 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.
    8. 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.
    9. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
    10. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
    11. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-40, September.
    12. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    13. K. Schmidt, 1999. "Reputation and Equilibrium Characterization in Repeated Games of Conflicting Interests," Levine's Working Paper Archive 626, David K. Levine.
    14. von Hayek, Friedrich August, 1989. "The Pretence of Knowledge," American Economic Review, American Economic Association, vol. 79(6), pages 3-7, December.
    15. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    16. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer, vol. 19(4), pages 431-56.
    17. 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.
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