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Type: Journal article
Title: Randomized switching in the two-envelope problem
Author: McDonnell, M.
Abbott, D.
Citation: Proceedings of the Royal Society of London Series A-Mathematical Physical and Engineering Sciences, 2009; 465(2111):3309-3322
Publisher: Royal Soc London
Issue Date: 2009
ISSN: 1364-5021
Statement of
Mark D. McDonnell and Derek Abbott
Abstract: The two-envelope problem is a conundrum in decision theory that is subject to longstanding debate. It is a counterintuitive problem of decidability between two different states, in the presence of uncertainty, where a player’s payoff must be maximized in some fashion. The problem is a significant one as it impacts on our understanding of probability theory, decision theory and optimization. It is timely to revisit this problem, as a number of related two-state switching phenomena are emerging in physics, engineering and economics literature. In this paper, we discuss this wider significance, and offer a new approach to the problem. For the first time, we analyse the problem by adopting Cover’s switching strategy—this is where we randomly switch states with a probability that is a smoothly decreasing function of the observed value of one state. Surprisingly, we show that the player’s payoff can be increased by this strategy. We also extend the problem to show that a deterministic switching strategy, based on a thresholded decision once the amount in an envelope is observed, is also workable.
Keywords: two-envelope problem; exchange paradox; optimal switching; cover switching; two-state random mixing; Parrondo’s principle
RMID: 0020092855
DOI: 10.1098/rspa.2009.0312
Grant ID:
Appears in Collections:Electrical and Electronic Engineering publications

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