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Common assumption of rationality

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  • Keisler, H. Jerome
  • Lee, Byung Soo

Abstract

In this paper, we provide an epistemic characterization of iterated admissibility (IA), i.e., iterated elimination of weakly dominated strategies. We show that rationality and common assumption of rationality (RCAR) in complete lexicographic type structures implies IA, and that there exist such structures in which RCAR can be satisfied. Our result is unexpected in light of a negative result in Brandenburger, Friedenberg, and Keisler (2008) (BFK) that shows the impossibility of RCAR in complete continuous structures. We also show that every complete structure with RCAR has the same types and beliefs as some complete continuous structure. This enables us to reconcile and interpret the difference between our results and BFK’s. Finally, we extend BFK’s framework to obtain a single structure that contains a complete structure with an RCAR state for every game. This gives a game-independent epistemic condition for IA.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 34441.

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Date of creation: 08 Sep 2011
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Handle: RePEc:pra:mprapa:34441

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Related research

Keywords: Epistemic game theory; rationality; admissibility; iterated weak dominance; assumption; completeness; Borel Isomorphism Theorem; o-minimality;

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References

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  1. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Equilibrium Refinements," Econometrica, Econometric Society, vol. 59(1), pages 81-98, January.
  2. Blume, Lawrence & Brandenburger, Adam & Dekel, Eddie, 1991. "Lexicographic Probabilities and Choice under Uncertainty," Econometrica, Econometric Society, vol. 59(1), pages 61-79, January.
  3. repec:stn:sotoec:0915 is not listed on IDEAS
  4. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  5. Paulo Barelli & Spyros Galanis, 2011. "Admissibility and Event-Rationality," RCER Working Papers 568, University of Rochester - Center for Economic Research (RCER).
  6. Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
  7. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  8. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
  9. Samuelson, Larry, 1992. "Dominated strategies and common knowledge," Games and Economic Behavior, Elsevier, vol. 4(2), pages 284-313, April.
  10. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2008. "Admissibility in Games," Econometrica, Econometric Society, vol. 76(2), pages 307-352, 03.
  11. Stahl, Dale O., 1995. "Lexicographic rationalizability and iterated admissibility," Economics Letters, Elsevier, vol. 47(2), pages 155-159, February.
  12. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
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Cited by:
  1. Paulo Barelli & Spyros Galanis, 2011. "Admissibility and Event-Rationality," RCER Working Papers 568, University of Rochester - Center for Economic Research (RCER).
  2. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.

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