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A Note On The Equivalence Of Rationalizability Concepts In Generalized Nice Games

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Author Info
ALEXANDER ZIMPER () (School of Economics, Faculty of Commerce, University of Cape Town, Private Bag, Rondebosch, 7701, Cape Town, RSA)

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Abstract

Moulin (1984) describes the class of nice games for which the solution concept of point-rationalizability coincides with iterated elimination of strictly dominated strategies. As a consequence nice games have the desirable property that all rationalizability concepts determine the same strategic solution. However, nice games are characterized by rather strong assumptions. For example, only single-valued best responses are admitted and the individual strategy sets have to be convex and compact subsets of the real line ℝ. This note shows that equivalence of all rationalizability concepts can be extended to multi-valued best response correspondences. The surprising finding is that equivalence does not hold for individual strategy sets that are compact and convex subsets of ℝn with n ≥ 2.

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Publisher Info
Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 08 (2006)
Issue (Month): 04 ()
Pages: 669-674
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Handle: RePEc:wsi:igtrxx:v:08:y:2006:i:04:p:669-674

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Related research
Keywords: Rationalizability; dominance solutions; nice games; JEL Classification: C72;

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Find related papers by JEL classification:
B4 - Schools of Economic Thought and Methodology - - Economic Methodology
C0 - Mathematical and Quantitative Methods - - General
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D5 - Microeconomics - - General Equilibrium and Disequilibrium
D7 - Microeconomics - - Analysis of Collective Decision-Making
M2 - Business Administration and Business Economics; Marketing; Accounting - - Business Economics

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.:

  1. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November. [Downloadable!] (restricted)
  2. Ghirardato, Paolo & Le Breton, Michel, 2000. "Choquet Rationality," Journal of Economic Theory, Elsevier, vol. 90(2), pages 277-285, February. [Downloadable!] (restricted)
  3. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
  4. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February. [Downloadable!] (restricted)
  5. R. Guesnerie, 2002. "Anchoring Economic Predictions in Common Knowledge," Econometrica, Econometric Society, vol. 70(2), pages 439-480, March. [Downloadable!] (restricted)
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(explanations, 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.)

  1. Alexander Zimper, 2006. "Assessing the Likelihood of Panic-Based Bank Runs," The B.E. Journal of Theoretical Economics, Berkeley Electronic Press, vol. 0(1). [Downloadable!]
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