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Characterizing the Strategic Impact of Misspecified Beliefs

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

Abstract

Previous research has established that the predictions of game theory are quite sensitive to the assumptions made about the players’ beliefs. We evaluate the severity of this robustness problem by characterizing conditions on the primitives of the model—the players’ beliefs and higher-order beliefs about the payoff-relevant parameters—for the behaviour of a given Harsanyi type to be approximated by the behaviour of (a sequence of) perturbed types. This amounts to providing belief-based characterizations of the strategic topologies of Dekel et al. (2006). We apply our characterizations to a variety of questions concerning robustness to perturbations of higher-order beliefs, including genericity of types that are consistent with a common prior, and we investigate the connections between our notions of robustness and the notion of common $p$-belief of Monderer and Samet (1989).

Suggested Citation

  • Yi-Chun Chen & Alfredo Di Tillio & Eduardo Faingold & Siyang Xiong, 2017. "Characterizing the Strategic Impact of Misspecified Beliefs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(4), pages 1424-1471.
    • Handle: RePEc:oup:restud:v:84:y:2017:i:4:p:1424-1471.
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    File URL: http://hdl.handle.net/10.1093/restud/rdw061
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    References listed on IDEAS

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    1. John K.-H. Quah & Bruno Strulovici, 2009. "Comparative Statics, Informativeness, and the Interval Dominance Order," Econometrica, Econometric Society, vol. 77(6), pages 1949-1992, November.
    2. Yi‐Chun Chen & Siyang Xiong, 2013. "Genericity and Robustness of Full Surplus Extraction," Econometrica, Econometric Society, vol. 81(2), pages 825-847, March.
    3. 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, March.
    4. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. , & , & , & ,, 2010. "Uniform topologies on types," Theoretical Economics, Econometric Society, vol. 5(3), September.
    6. Morris, Stephen, 1994. "Trade with Heterogeneous Prior Beliefs and Asymmetric Information," Econometrica, Econometric Society, vol. 62(6), pages 1327-1347, November.
    7. Dov Monderer & Dov Samet, 1996. "Proximity of Information in Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 707-725, August.
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    Cited by:

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    2. Heifetz, Aviad & Kets, Willemien, 2018. "Robust multiplicity with a grain of naiveté," Theoretical Economics, Econometric Society, vol. 13(1), January.
    3. Aviad Heifetz, 2019. "Robust multiplicity with (transfinitely) vanishing naiveté," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1277-1296, December.

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    More about this item

    Keywords

    Games with incomplete information; Rationalizability; Higher-order beliefs; Robustness;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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