Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/217076 
Year of Publication: 
2020
Citation: 
[Journal:] Theoretical Economics [ISSN:] 1555-7561 [Volume:] 15 [Issue:] 1 [Publisher:] The Econometric Society [Place:] New Haven, CT [Year:] 2020 [Pages:] 89-122
Publisher: 
The Econometric Society, New Haven, CT
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 ICRλ, where λ is a sequence whose term λn is the probability players attach to (n- 1)th-order belief in rationality. We find that Weinstein and Yildiz's discontinuity remains when λn is above an appropriate threshold for all n, but fails when λn 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.
Subjects: 
Robustness
rationalizability
bounded rationality
incomplete information
belief hierarchies
JEL: 
C72
D82
D83
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by-nc Logo
Document Type: 
Article

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