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

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