Nonstationary Nonzero-Sum Markov Games Under a Probability Criterion

Xin Guo () and Xin Wen
Additional contact information
Xin Guo: School of Science, Sun Yat-sen University, Guangzhou 510275, P. R. China
Xin Wen: School of Science, Sun Yat-sen University, Guangzhou 510275, P. R. China

International Game Theory Review (IGTR), 2025, vol. 27, issue 03, 1-32

Abstract: This paper deals with N-person nonzero-sum discrete-time Markov games under a probability criterion, in which the transition probabilities and reward functions are allowed to vary with time. Differing from the existing works on the expected reward criteria, our concern here is to maximize the probabilities that the accumulated rewards until the first passage time to any target set exceed a given goal, which represent the reliability of the players’ income. Under a mild condition, by developing a comparison theorem for the probability criterion, we prove the existence of a Nash equilibrium over history-dependent policies. Moreover, we provide an efficient algorithm for computing 𠜖-Nash equilibria. Finally, we illustrate our main results by a nonstationary energy management model and take a numerical experiment.

Keywords: Nonstationary nonzero-sum stochastic game; probability criterion; comparison theorem; optimality equations; Nash equilibrium; algorithm for 𠜖-Nash equilibrium (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219198925300028
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:igtrxx:v:27:y:2025:i:03:n:s0219198925300028

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219198925300028

Access Statistics for this article

International Game Theory Review (IGTR) is currently edited by David W K Yeung

More articles in International Game Theory Review (IGTR) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().