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Rational behavior under correlated uncertainty

Listed author(s):
  • Frick, Mira
  • Romm, Assaf

In complete information games, Dekel and Fudenberg (1990) and Börgers (1994) have proposed the solution concept S∞W (one round of elimination of weakly dominated strategies followed by iterated elimination of strongly dominated strategies), motivating it by a characterization in terms of “approximate common certainty” of admissibility. We examine the validity of this characterization of S∞W in an incomplete information setting. We argue that in Bayesian games with a nontrivial state space, the characterization is very sensitive to the way in which uncertainty in the form of approximate common certainty of admissibility is taken to interact with the uncertainty already captured by players' beliefs about the states of nature: We show that S∞W corresponds to approximate common certainty of admissibility when this is not allowed to coincide with any changes to players' beliefs about states. If approximate common certainty of admissibility is accompanied by vanishingly small perturbations to beliefs, then S∞W is a (generally strict) subset of the predicted behavior, which we characterize in terms of a generalization of Hu's (2007) perfect p-rationalizable set.

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File URL: http://www.sciencedirect.com/science/article/pii/S0022053115001684
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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 160 (2015)
Issue (Month): C ()
Pages: 56-71

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Handle: RePEc:eee:jetheo:v:160:y:2015:i:c:p:56-71
DOI: 10.1016/j.jet.2015.08.009
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Frank Schuhmacher, 1999. "Proper rationalizability and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 599-615.
  2. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
  3. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October.
  4. Hu, Tai-Wei, 2007. "On p-rationalizability and approximate common certainty of rationality," Journal of Economic Theory, Elsevier, vol. 136(1), pages 379-391, September.
  5. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
  6. Fudenberg, Drew & Kreps, David M. & Levine, David K., 1988. "On the robustness of equilibrium refinements," Journal of Economic Theory, Elsevier, vol. 44(2), pages 354-380, April.
  7. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41 World Scientific Publishing Co. Pte. Ltd..
  8. 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.
  9. Dekel, Eddie & Fudenberg, Drew, 1990. "Rational behavior with payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 52(2), pages 243-267, December.
  10. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
  11. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, 03.
  12. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
  13. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
  14. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212 World Scientific Publishing Co. Pte. Ltd..
  15. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
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