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

Fabrizio Germano (), Jonathan Weinstein and Peio Zuazo-Garin

No 947, Working Papers from Barcelona Graduate School of Economics

Abstract: Predictions under common knowledge of payoffs may differ from those under arbi- trarily, 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?, where ? is a sequence whose nth 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 ?), but fails when higher-order belief in rationality eventually becomes low enough (? 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: 2017-01
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
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Related works:
Journal Article: Uncertain rationality, depth of reasoning and robustness in games with incomplete information (2020) Downloads
Working Paper: Uncertain Rationality, Depth of Reasoning and Robustness in Games with Incomplete Information (2016) Downloads
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