Nash equilibria in a class of Markov stopping games with total reward criterion

Rolando Cavazos-Cadena (), Mario Cantú-Sifuentes and Imelda Cerda-Delgado
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Rolando Cavazos-Cadena: Universidad Autónoma Agraria Antonio Narro
Mario Cantú-Sifuentes: Universidad Autónoma Agraria Antonio Narro
Imelda Cerda-Delgado: Universidad Autónoma Agraria Antonio Narro

Mathematical Methods of Operations Research, 2021, vol. 94, issue 2, No 6, 319-340

Abstract: Abstract This work is concerned with a class of discrete-time, zero-sum games with Markov transitions on a denumerable state space. At each decision time player II can stop the system paying a terminal reward to player I, or can let the system 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. The performance of a pair of decision strategies is measured by the total expected reward criterion and, under mild continuity-compactness conditions, communication-ergodicity properties are used to show that (i) the upper and lower value functions of the game coincide, and (ii) their common value is characterized as the unique fixed point of a nonexpansive operator from which a Nash equilibrium can be derived.

Keywords: Equality of the upper and lower value functions; Monotonicity property; Hitting time; Stationary strategy; Bounded rewards; 91A10; 91A15 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00186-021-00759-5

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