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February, 1995 A Stochastic Game of Optimal Stopping and Order Selection
Alexander V. Gnedin, Ulrich Krengel
Ann. Appl. Probab. 5(1): 310-321 (February, 1995). DOI: 10.1214/aoap/1177004842


We study the following two-person zero-sum game. $n$ random numbers are drawn independently from a continuous distribution known to both players. Player 2 observes all the numbers and selects an order to present them to the opponent. Player 1 learns the numbers sequentially as they are presented and may stop learning whenever he/she pleases. If the stop occurred at the number that is the $k$th largest among all $n$ numbers, Player 1 pays the amount $q(k)$ to Player 2, where $q(1) \leq \cdots \leq q(n)$ is a given payoff function. Player 1 aims to minimize the expected payoff; Player 2 aims to maximize it. We find an explicit solution of the game for a wide class of payoff functions including those $q$'s typically considered in the context of best choice problems.


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Alexander V. Gnedin. Ulrich Krengel. "A Stochastic Game of Optimal Stopping and Order Selection." Ann. Appl. Probab. 5 (1) 310 - 321, February, 1995.


Published: February, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0824.62079
MathSciNet: MR1325055
Digital Object Identifier: 10.1214/aoap/1177004842

Primary: 60G40

Keywords: arrangement , best-choice problem , minimax strategy , Optimal stopping , order selection , ‎rank‎

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.5 • No. 1 • February, 1995
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