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An algorithm for proper rationalizability

  • Perea, Andrés
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    Proper rationalizability ([Schuhmacher, 1999] and [Asheim, 2001]) is a concept in epistemic game theory based on the following two conditions: (a) a player should be cautious, that is, should not exclude any opponent's strategy from consideration; and (b) a player should respect the opponents' preferences, that is, should deem an opponent's strategy si infinitely more likely than if he believes the opponent to prefer si to . A strategy is properly rationalizable if it can optimally be chosen under common belief in the events (a) and (b). In this paper we present an algorithm that for every finite game computes the set of all properly rationalizable strategies. The algorithm is based on the new idea of a preference restriction, which is a pair (si,Ai) consisting of a strategy si, and a subset of strategies Ai, for player i. The interpretation is that player i prefers some strategy in Ai to si. The algorithm proceeds by successively adding preference restrictions to the game.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0899825610001715
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    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 72 (2011)
    Issue (Month): 2 (June)
    Pages: 510-525

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    Handle: RePEc:eee:gamebe:v:72:y:2011:i:2:p:510-525
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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    1. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2008. "Admissibility in Games," Econometrica, Econometric Society, vol. 76(2), pages 307-352, 03.
    2. E. Dekel & D. Fudenberg, 2010. "Rational Behavior with Payoff Uncertainty," Levine's Working Paper Archive 379, David K. Levine.
    3. Tan, Tommy Chin-Chiu & da Costa Werlang, Sergio Ribeiro, 1988. "The Bayesian foundations of solution concepts of games," Journal of Economic Theory, Elsevier, vol. 45(2), pages 370-391, August.
    4. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
    5. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
    6. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    7. Frank Schuhmacher, 1999. "Proper rationalizability and backward induction," International Journal of Game Theory, Springer, vol. 28(4), pages 599-615.
    8. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
    9. Stahl, Dale O., 1995. "Lexicographic rationalizability and iterated admissibility," Economics Letters, Elsevier, vol. 47(2), pages 155-159, February.
    10. Geir B. Asheim, 2002. "Proper rationalizability in lexicographic beliefs," International Journal of Game Theory, Springer, vol. 30(4), pages 453-478.
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