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

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

Working paper
Author/s: 
Fabrizio Germano, Jonathan Weinstein and Peio Zuazo-Garin
Issue number: 
947
Series: 
Barcelona GSE Working Paper
Publisher: 
Barcelona Graduate School of Economics
Year: 
2017
Working paper [1]
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 ICRλ, where λ 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 λ), but fails when higher-order belief in rationality eventually becomes low enough (λ converging to 0).
Tags: 
Game Theory & Graphs [2]

Source URL:http://www.coalitiontheory.net/content/uncertain-rationality-depth-reasoning-and-robustness-games-incomplete-information

Links
[1] http://research.barcelonagse.eu/file/5600/download?token=kDGoQOyo [2] http://www.coalitiontheory.net/research-areas/game-theory-graphs