Gain from the two-envelope problem via information asymmetry: on the suboptimality of randomized switching

Simple item page
dc.contributor.authorMcDonnell, M.
dc.contributor.authorGrant, A.
dc.contributor.authorLand, I.
dc.contributor.authorVellambi, B.
dc.contributor.authorAbbott, D.
dc.contributor.authorLever, K.
dc.date.issued2011
dc.description.abstractThe 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.
dc.description.statementofresponsibilityMark D. McDonnell, Alex J. Grant, Ingmar Land, Badri N. Vellambi, Derek Abbott and Ken Lever
dc.identifier.citationProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2011; 467(2134):2825-2851
dc.identifier.doi10.1098/rspa.2010.0541
dc.identifier.issn1364-5021
dc.identifier.issn1471-2946
dc.identifier.orcidMcDonnell, M. [0000-0002-7009-3869]
dc.identifier.orcidAbbott, D. [0000-0002-0945-2674]
dc.identifier.urihttp://hdl.handle.net/2440/70002
dc.language.isoen
dc.publisherRoyal Soc London
dc.relation.granthttp://purl.org/au-research/grants/arc/DP1093425
dc.relation.granthttp://purl.org/au-research/grants/arc/DP1093425
dc.rightsThis journal is © 2011 The Royal Society
dc.source.urihttps://doi.org/10.1098/rspa.2010.0541
dc.subjecttwo-envelope problem
dc.subjecttwo-envelope paradox
dc.subjectexchange paradox
dc.subjectgame theory
dc.subjectrandomized switching
dc.subjectinformation asymmetry
dc.titleGain from the two-envelope problem via information asymmetry: on the suboptimality of randomized switching
dc.typeJournal article
pubs.publication-statusPublished

Files

Collections

Electrical and Electronic Engineering publications