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Title: Markov stopping games with an absorbing state and total reward criterion (English)
Author: Cavazos-Cadena, Rolando
Author: Rodríguez-Gutiérrez, Luis
Author: Sánchez-Guillermo, Dulce María
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 57
Issue: 3
Year: 2021
Pages: 474-492
Summary lang: English
Category: math
Summary: This work is concerned with discrete-time zero-sum games with Markov transitions on a denumerable space. At each decision time player II can stop the system paying a terminal reward to player I, or can let the system to continue its evolution. If the system is not halted, player I selects an action which affects the transitions and receives a running reward from player II. Assuming the existence of an absorbing state which is accessible from any other state, the performance of a pair of decision strategies is measured by the total expected reward criterion. In this context it is shown that the value function of the game is characterized by an equilibrium equation, and the existence of a Nash equilibrium is established. (English)
Keyword: non-expansive operator
Keyword: monotonicity property
Keyword: fixed point
Keyword: equilibrium equation
Keyword: hitting time
Keyword: bounded rewards
MSC: 91A10
MSC: 91A15
idZBL: Zbl 07442520
idMR: MR4299459
DOI: 10.14736/kyb-2021-3-0474
Date available: 2021-11-04T12:46:26Z
Last updated: 2022-02-24
Stable URL:
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