Uncertain rationality and robustness in games with incomplete information

Fabrizio Germano and Peio Zuazo-Garin

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

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.

Keywords: Robustness; rationalizability; uncertain rationality; incomplete information; belief hierarchies. (search for similar items in EconPapers)
JEL-codes: C72 D82 D83 (search for similar items in EconPapers)
Date: 2015-02
New Economics Papers: this item is included in nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Working Paper: Uncertain Rationality and Robustness in Games with Incomplete Information (2015)
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