The best choice problem with random arrivals: How to beat the 1/e-strategy

Alexander Gnedin

Stochastic Processes and their Applications, 2022, vol. 145, issue C, 226-240

Abstract: In the best choice problem with random arrivals, an unknown number n of rankable items arrive at times sampled from the uniform distribution. As is well known, a real-time player can ensure stopping at the overall best item with probability at least 1/e, by waiting until time 1/e then selecting the first relatively best item (record) to appear, if available. This paper discusses the issue of dominance in a wide class of multi-cutoff stopping strategies of best choice, and argues that in fact the player faces a trade-off between success probabilities for various values of n. We show that the 1/e-strategy is not a unique minimax strategy and that it can be improved in various ways.

Keywords: Best choice problem; Optimal stopping; Random arrivals; 1/e-strategy; Minimax strategy; Dominance (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2021.12.008

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