A STOCHASTIC GAME OF OPTIMAL STOPPING AND ORDER SELECTION
成果类型：
Article
署名作者：
Gnedin, Alexander V.; Krengel, Ulrich
署名单位：
University of Gottingen
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004842
发表日期：
1995
页码：
310-321
关键词：
摘要：
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 kth largest among all n numbers, Player 1 pays the amount q(k) to Player 2, where q(1) <= ... <= 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.