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Double stopping by two decision-makers

Part of: Stochastic processes

Published online by Cambridge University Press:  01 July 2016

K. Szajowski
K. Szajowski*
Affiliation:
Delft University of Technology
*
∗Permanent address: Institute of Mathematics, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, PL-50-370 Wroclaw, Poland.
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Abstract

A problem of optimal stopping of the discrete-time Markov process by two decision-makers (Player 1 and Player 2) in a competitive situation is considered. The zero-sum game structure is adopted. The gain function depends on states chosen by both decision-makers. When both players want to accept the realization of the Markov process at the same moment, the priority is given to Player 1. The construction of the value function and the optimal strategies for the players are given. The Markov chain case is considered in detail. An example related to the generalized secretary problem is solved.

Keywords

OPTIMAL STOPPINGGAME VARIANTMARKOV PROCESSSECRETARY PROBLEMZERO-SUM TWO-PERSON GAME: PRIORITY OF THE PLAYERS

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 2 , June 1993 , pp. 438 - 452
Copyright
Copyright © Applied Probability Trust 1993 

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Footnotes

Research partially supported by the Research Fellowship Committee of Delft University of Technology, while the author was visiting the Faculty of Technical Mathematics and Informatics there.

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