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An Optimal Threshold Strategy in the Two-Envelope Problem with Partial Information

Part of:Mathematical economicsStochastic processes

Published online by Cambridge University Press:  30 January 2018

Martin Egozcue and
Luis Fuentes García
Martin Egozcue*
Affiliation:
Universidad de la República de Uruguay
Luis Fuentes García*
Affiliation:
Universidade da Coruña
*
∗ Postal address: Department of Economics, Facultad de Ciencias Sociales, Universidad de la República de Uruguay, Montevideo, 11600, Uruguay. Email address: egozcuemj@gmail.com
∗∗ Postal address: Departamento de Métodos Matemáticos y de Representacioón, Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos, Universidade da Coruña, 15071 A Coruña, Spain.
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Abstract

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In this paper we propose a strategy that gives an optimal lower bound of the average gain for the two-envelope problem within the McDonnell and Abbott (2009) and McDonnell et al. (2011) framework. We obtain this result with partial information about the probability distribution of the envelope's contents.

Keywords

Two-envelope problemthreshold strategydecision theory

MSC classification

Primary:91B06: Decision theory
Secondary:60G40: Stopping times; optimal stopping problems; gambling theory

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 1 , March 2015, pp. 298 - 304
Copyright
© Applied Probability Trust 

References

Allison, A. and Abbott, D. (2001). Control systems with stochastic feedback. Chaos 11, 715–724.CrossRefGoogle ScholarPubMed
Brams, S. J. and Kilgour, D. M. (1995). The box problem: to switch or not to switch. Math. Magazine 68, 27–34.Google Scholar
Christensen, R. and Utts, J. (1992). Bayesian resolution of the ‘exchange paradox’. Amer. Statistician 46, 274–276.Google Scholar
Egozcue, M., Fuentes, Garcı´a L. and Zitikis, R. (2013). An optimal strategy for maximizing the expected real-estate selling price: accept or reject an offer? J. Statist. Theory Practice 7, 596–609.CrossRefGoogle Scholar
Gardner, M. (1982). Aha! Gotcha: Paradoxes to Puzzle and Delight. W. H. Freeman, San Francisco, CA.Google Scholar
Kraitchik, M. (1930). Le paradoxe des cravates. In La Mathematique des Jeux, Imprimerie Stevens Frères, Bruxelles.Google Scholar
McDonnell, M. D. and Abbott, D. (2009). Randomized switching in the two-envelope problem. Proc. R. Soc. London A 465, 3309–3322.Google Scholar
McDonnell, M. D. et al. (2011). Gain from the two-envelope problem via information asymmetry: on the suboptimality of randomized switching. Proc. R. Soc. London A 467, 2825–2851.Google Scholar
Nalebuff, B. (1989). Puzzles: the other person's envelope is always greener. J. Econom. Perspectives 3, 171–181.Google Scholar
Scarf, H. (1958). A min-max solution of an inventory problem. In Studies in the Mathematical Theory of Inventory and Production, Stanford University Press, pp. 201–209.Google Scholar