An algorithm for proper rationalizability
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Stahl, Dale O., 1995. "Lexicographic rationalizability and iterated admissibility," Economics Letters, Elsevier, vol. 47(2), pages 155-159, February.
- Dekel, Eddie & Fudenberg, Drew, 1990.
"Rational behavior with payoff uncertainty,"
Journal of Economic Theory,
Elsevier, vol. 52(2), pages 243-267, December.
- Geir B. Asheim, 2002. "Proper rationalizability in lexicographic beliefs," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 453-478.
- Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
- Werlang, Sérgio Ribeiro da Costa & Chin-Chiu Tan, Tommy, 1987.
"The Bayesian Foundations of solution concepts of games,"
Economics Working Papers (Ensaios Economicos da EPGE)
111, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
- 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.
- Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
- Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2008.
"Admissibility in Games,"
Econometric Society, vol. 76(2), pages 307-352, 03.
- Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
- Lawrence Blume & Adam Brandenburger & Eddie Dekel, 2014.
"Lexicographic Probabilities and Choice Under Uncertainty,"
World Scientific Book Chapters,
in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 6, pages 137-160
World Scientific Publishing Co. Pte. Ltd..
- Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
- Frank Schuhmacher, 1999. "Proper rationalizability and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 599-615.
When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:72:y:2011:i:2:p:510-525. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.