Paper #1548

Title:

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

Authors:

Fabrizio Germano, Jonathan Weinstein and Peio Zuazo-Garin

Date:

December 2016

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.

JEL codes:

C72, D82, D83.

Area of Research:

Microeconomics

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