An optimal threshold strategy in the two-envelope problem with partial information. (English) Zbl 1312.91040

Egozcue, Martin; Fuentes García, Luis

J. Appl. Probab. 52, No. 1, 298-304 (2015).

Summary: We propose a strategy that gives an optimal lower bound of the average gain for the two-envelope problem within the framework of [M. D. McDonnell and D. Abbott, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 465, No. 2111, 3309–3322 (2009; Zbl 1186.91071); M. D. McDonnell et al., Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 467, No. 2134, 2825–2851 (2011; Zbl 1237.91077)]. We obtain this result with partial information about the probability distribution of the envelope’s contents.

MSC:

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

Keywords:

two-envelope problem; threshold strategy; decision theory

Citations:

Zbl 1186.91071; Zbl 1237.91077