Uncertain Rationality, Depth of Reasoning and Robustness in Games with Incomplete Information

Fabrizio Germano, Jonathan Weinstein and Peio Zuazo-Garin

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

Abstract: Predictions under common knowledge of payoffs may differ from those under arbitrarily, but finitely, many orders of mutual knowledge; Rubinstein's (1989) Email game is a seminal example. Weinstein and Yildiz (2007) showed that the discontinuity in the example generalizes: for all types with multiple rationalizable (ICR) actions, there exist similar types with unique rationalizable action. This paper studies how a wide class of departures from common belief in rationality impact Weinstein and Yildiz's discontinuity. We weaken ICR to ICR-x, where x is a sequence whose n-th term is the probability players attach to (n - 1)th-order belief in rationality. We find that Weinstein and Yildiz's discontinuity holds when higher-order belief in rationality remains above some threshold (constant x), but fails when higher-order belief in rationality eventually becomes low enough (x converging to 0).

Keywords: Robustness; rationalizability; bounded rationality; incomplete information; belief hierarchies. (search for similar items in EconPapers)
JEL-codes: C72 D82 D83 (search for similar items in EconPapers)
Date: 2016-12
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
References: View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Related works:
Journal Article: Uncertain rationality, depth of reasoning and robustness in games with incomplete information (2020)
Working Paper: Uncertain Rationality, Depth of Reasoning and Robustness in Games with Incomplete Information (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:1548

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