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Regular version of the site

Article

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

Theoretical Economics. 2020. Vol. 15. P. 89-122.
Germano F., Weinstein J., Zuazo-Garin P.

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-lambda, where lambda 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 remains when lambda_n is above an appropriate threshold for all n, but fails when lambda converges to 0. That is, if players' confidence in mutual rationality persists at high orders, the discontinuity persists, but if confidence vanishes at high orders, the discontinuity vanishes.