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The equivalence of the Dekel-Fudenberg iterative procedure and weakly perfect rationalizability

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  • Vincent J. Vannetelbosch

    (CORE, University of Louvain, voie du Roman Pays 34, B-1348 Louvain-la-Neuve, BELGIUM)

  • P. Jean-Jacques Herings

    ()
    (Department of Economics, University of Maastricht, Postbus 616, NL-6200 Maastricht,THE NETHERLANDS)

Abstract

Two approaches have been proposed in the literature to refine the rationalizability solution concept: either assuming that a player believes that with small probability her opponents choose strategies that are irrational, or assuming that their is a small amount of payoff uncertainty. We show that both approaches lead to the same refinement if strategy perturbations are made according to the concept of weakly perfect rationalizability, and if there is payoff uncertainty as in Dekel and Fudenberg [J. of Econ. Theory 52 (1990), 243-267]. For both cases, the strategies that survive are obtained by starting with one round of elimination of weakly dominated strategies followed by many rounds of elimination of strictly dominated strategies.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 15 (2000)
Issue (Month): 3 ()
Pages: 677-687

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Handle: RePEc:spr:joecth:v:15:y:2000:i:3:p:677-687

Note: Received: 10 December 1998; revised version: 26 April 1999
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Keywords: Rationalizability; Refinements.;

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  1. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  2. Ben-Porath, Elchanan, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," Review of Economic Studies, Wiley Blackwell, vol. 64(1), pages 23-46, January.
  3. HERINGS, P. Jean-Jacques & ANNETELBOSCH, Vincent J., . "Refinements of rationalizability for normal-form games," CORE Discussion Papers RP -1378, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
  5. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  6. Gul, Faruk, 1996. "Rationality and Coherent Theories of Strategic Behavior," Journal of Economic Theory, Elsevier, vol. 70(1), pages 1-31, July.
  7. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
  8. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
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Cited by:
  1. Grandjean Gilles & Mauleon Ana & Vannetelbosch Vincent, 2009. "Strongly Rational Sets for Normal-Form Games," Research Memorandum 059, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  2. MAULEON, Ana & VANNETELBOSCH, Vincent J., . "Bargaining with endogenous deadlines," CORE Discussion Papers RP -1719, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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