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The Strategic Impact of Higher-Order Beliefs

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  • Yi-Chun Chen
  • Alfredo Di Tillio
  • Eduardo Faingold
  • Siyang Xiong

Abstract

Previous research has established that the predictions made by game theory about strategic behavior in incomplete information games are quite sensitive to the assumptions made about the players' infinite hierarchies of beliefs. We evaluate the severity of this robustness problem by characterizing conditions on the primitives of the model -- the players’ hierarchies of beliefs -- for the strategic behavior of a given Harsanyi type to be approximated by the strategic behavior of (a sequence of) perturbed types. This amounts to providing characterizations of the strategic topologies of Dekel, Fudenberg, and Morris (2006) in terms of beliefs. We apply our characterizations to a variety of questions concerning robustness to perturbations of higher-order beliefs, including genericity of common priors, and the connections between robustness of strategic behavior and the notion of common p-belief of Monderer and Samet (1989).

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000517.

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Date of creation: 11 Sep 2012
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Handle: RePEc:cla:levarc:786969000000000517

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  1. Xiong, Siyang & Chen, Yi-Chun & di Tillio, Alfredo & Faingold, Eduardo, 2010. "Uniform topologies on types," Theoretical Economics, Econometric Society, vol. 5(3), September.
  2. Aviad Heifetz & Zvika Neeman, 2006. "On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design," Econometrica, Econometric Society, vol. 74(1), pages 213-233, 01.
  3. Zvika Neeman, 1993. "A Note on Approximating Agreeing to Disagree Results with Common p-Beliefs," Discussion Papers 1029, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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.
  5. Dirk Bergemann & Stephen Morris, 2009. "Robust Implementation in Direct Mechanisms," Levine's Working Paper Archive 814577000000000109, David K. Levine.
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Cited by:
  1. Dirk Bergemann & Stephen Morris & Satoru Takahashi, 2011. "Interdependent Preferences and Strategic Distinguishability," Levine's Working Paper Archive 786969000000000054, David K. Levine.
  2. Chen, Yi-Chun & Xiong, Siyang, 2013. "The e-mail game phenomenon," Games and Economic Behavior, Elsevier, vol. 80(C), pages 147-156.

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