Open AccessTwo-person zero-sum stochastic games with varying discount factors
Author(s) -
X. G. Wu,
Qi Wang,
Yinying Kong,
Guangzhou Economics
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021668
Subject(s) - mathematics , zero (linguistics) , markov chain , discounting , zero sum game , state space , mathematical economics , banach space , action (physics) , space (punctuation) , markov decision process , function (biology) , discrete mathematics , combinatorics , mathematical optimization , markov process , economics , nash equilibrium , statistics , computer science , finance , philosophy , linguistics , physics , quantum mechanics , evolutionary biology , biology , operating system
In this paper, two-person zero-sum Markov games with Borel state space and action space, unbounded reward function and state-dependent discount factors are studied. The optimal criterion is expected discount criterion. Firstly, sufficient conditions for the existence of optimal policies are given for the two-person zero-sum Markov games with varying discount factors. Then, the existence of optimal policies is proved by Banach fixed point theorem. Finally, we give an example for reservoir operations to illustrate the existence results.