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Type: Journal article
Title: Gain from the two-envelope problem via information asymmetry: on the suboptimality of randomized switching
Author: McDonnell, M.
Grant, A.
Land, I.
Vellambi, B.
Abbott, D.
Lever, K.
Citation: Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 2011; 467(2134):2825-2851
Publisher: Royal Soc London
Issue Date: 2011
ISSN: 1364-5021
Statement of
Mark D. McDonnell, Alex J. Grant, Ingmar Land, Badri N. Vellambi, Derek Abbott and Ken Lever
Abstract: The two-envelope problem (or exchange problem) is one of maximizing the payoff in choosing between two values, given an observation of only one. This paradigm is of interest in a range of fields from engineering to mathematical finance, as it is now known that the payoff can be increased by exploiting a form of information asymmetry. Here, we consider a version of the 'two-envelope game' where the envelopes’ contents are governed by a continuous positive random variable. While the optimal switching strategy is known and deterministic once an envelope has been opened, it is not necessarily optimal when the content's distribution is unknown. A useful alternative in this case may be to use a switching strategy that depends randomly on the observed value in the opened envelope. This approach can lead to a gain when compared with never switching. Here, we quantify the gain owing to such conditional randomized switching when the random variable has a generalized negative exponential distribution, and compare this to the optimal switching strategy. We also show that a randomized strategy may be advantageous when the distribution of the envelope's contents is unknown, since it can always lead to a gain.
Keywords: two-envelope problem; two-envelope paradox; exchange paradox; game theory; randomized switching; information asymmetry
Rights: This journal is © 2011 The Royal Society
RMID: 0020112368
DOI: 10.1098/rspa.2010.0541
Grant ID:
Appears in Collections:Electrical and Electronic Engineering publications

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