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Uncertain rationality and robustness in games with incomplete information

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Abstract

Economic predictions are highly sensitive to model and informational specifications. Weinstein and Yildiz (2007) show that, in static games with incomplete information, only very weak predictions, namely, the interim correlated rationalizable (ICR) actions, are robust to higher-order belief misspecifications. This paper extends their robustness analysis to allow for higher-order uncertainty about rationality. We introduce interim correlated p-rationalizability (ICRp) as a solution concept for games with incomplete information. We first confirm the robustness of the ICR predictions to small departures from common belief in rationality by showing the continuity of ICRp actions at p = 1, where they coincide with ICR. At the same time, we show that Weinstein and Yildiz's (2007) deeper results on the structure of rationalizability, most notably, their discontinuity and generic local uniqueness properties, fail as soon as any arbitrarily small amount of higher-order uncertainty about rationality is introduced. Thus, we find that common belief in rationality is a necessary condition for Weinstein and Yildiz's (2007) discontinuity property to hold. Among other things, this reveals the diminishing strategic impact of higher-order belief constraints.

Suggested Citation

  • Fabrizio Germano & Peio Zuazo-Garin, 2015. "Uncertain rationality and robustness in games with incomplete information," Economics Working Papers 1470, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1470
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    1. 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.
    2. ,, 2013. "On the structure of rationalizability for arbitrary spaces of uncertainty," Theoretical Economics, Econometric Society, vol. 8(2), May.
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    Cited by:

    1. Fabrizio Germano & Peio Zuazo-Garin, 2017. "Bounded rationality and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 595-629, August.

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    More about this item

    Keywords

    Robustness; rationalizability; uncertain rationality; incomplete information; belief hierarchies.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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