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https://hdl.handle.net/2440/70002
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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 A: Mathematical, Physical and Engineering Sciences, 2011; 467(2134):2825-2851 |
Publisher: | Royal Soc London |
Issue Date: | 2011 |
ISSN: | 1364-5021 1471-2946 |
Statement of Responsibility: | 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 |
DOI: | 10.1098/rspa.2010.0541 |
Grant ID: | http://purl.org/au-research/grants/arc/DP1093425 http://purl.org/au-research/grants/arc/DP1093425 |
Published version: | http://dx.doi.org/10.1098/rspa.2010.0541 |
Appears in Collections: | Aurora harvest 5 Electrical and Electronic Engineering publications |
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