Uncertain rationality, depth of reasoning and robustness in games with incomplete information

Germano, Fabrizio; Weinstein, Jonathan; Zuazo-Garin, Peio

Uncertain rationality, depth of reasoning and robustness in games with incomplete information

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Germano, F, Weinstein, J, Zuazo-Garin, P. Uncertain rationality, depth of reasoning and robustness in games with incomplete information. 2016. handle: http://hdl.handle.net/10230/27992

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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).