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The Equivalence of the Dekel-Fudenberg Iterative Procedure and Weakly Perfect Rationalizability

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  • P. Jean-Jacques Herings

    (Dept. Econometrics & Center, Tilburg Univ.)

  • Vincent J. Vannetelbosch

    (IEP, Basque Country University)

Abstract

Two approaches have been proposed in the literature to refine the rationalizability solution concept: either assuming that players make small errors when playing their strategies, or assuming that there is a small amount of payoff uncertainty. We show that both approaches lead to the same refinement if errors are made according to the concept of weakly perfect rationalizability, and there is payoff uncertainty as in Dekel and Fudenberg [Journal of Economic 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

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1173.

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Length: 11 pages
Date of creation: Mar 1998
Date of revision:
Publication status: Published in Economic Theory (2000), 15(2): 677-687
Handle: RePEc:cwl:cwldpp:1173

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Keywords: Rationalizability; refinements;

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References

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  1. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  2. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
  3. Herings, P.J.J. & Vannetelbosch, V., 1997. "Refinements of Rationalizability for Normal-Form Games," Discussion Paper 1997-03, Tilburg University, Center for Economic Research.
  4. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  5. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  6. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
  7. Gul, Faruk, 1996. "Rationality and Coherent Theories of Strategic Behavior," Journal of Economic Theory, Elsevier, vol. 70(1), pages 1-31, July.
  8. 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.
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Cited by:
  1. Ana MAULEON & Vincent J. VANNETELBOSCH, 2001. "Bargaining with Endogenous Deadlines," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001021, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  2. GRANDJEAN, Gilles & MAULEON, Ana & VANNETELBOSCH, Vincent, 2009. "Strongly rational sets for normal-form games," CORE Discussion Papers 2009066, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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