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Subjective Games and Equilibria

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  • Kalai, Ehud
  • Lehrer, Ehud

Abstract

Applying the concepts of Nash, Bayesian or correlated equilibrium to 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 subjective Nash and correlated equilibria, replace unavailable objective knowledge by subjective assessments. When playing such a game repeatedly, subjective optimizers will converge to a subjective equilibrium. We apply this approach to some well known examples including a single multi-arm bandit player, multi-person mulit-arm bandit games, and repeated Cournot oligopoly games.
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Suggested Citation

  • Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Games and Equilibria," Working Papers 875, California Institute of Technology, Division of the Humanities and Social Sciences.
    • Handle: RePEc:clt:sswopa:875
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    References listed on IDEAS

    as
    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, 1995. "Case-Based Decision Theory," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 605-639.
    3. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
    4. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
    5. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
    6. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
    7. Sylvain Sorin, 1992. "Information and Rationality : Some Comments," Annals of Economics and Statistics, GENES, issue 25-26, pages 315-325.
    8. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    9. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    10. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
    11. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    12. von Hayek, Friedrich August, 1989. "The Pretence of Knowledge," American Economic Review, American Economic Association, vol. 79(6), pages 3-7, December.
    13. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    14. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 431-456.
    15. Crawford, Vincent P & Haller, Hans, 1990. "Learning How to Cooperate: Optimal Play in Repeated Coordination Games," Econometrica, Econometric Society, vol. 58(3), pages 571-595, May.
    16. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    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 1231-1240, September.
    19. Porter, Robert H., 1983. "Optimal cartel trigger price strategies," Journal of Economic Theory, Elsevier, vol. 29(2), pages 313-338, April.
    20. repec:adr:anecst:y:1992:i:25-26:p:15 is not listed on IDEAS
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    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods

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