Marginal Values of a Stochastic Game
成果类型：
Article
署名作者：
Attia, Luc; Oliu-Barton, Miquel; Saona, Raimundo
署名单位：
Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Institute of Science & Technology - Austria
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.2023.0297
发表日期：
2025
关键词：
摘要：
Zero -sum stochastic games are parameterized by payoffs, transitions, and possibly a discount rate. In this article, we study how the main solution concepts, the discounted and undiscounted values, vary when these parameters are perturbed. We focus on the marginal values, introduced by Mills in 1956 in the context of matrix games-that is, the directional derivatives of the value along any fixed perturbation. We provide a formula for the marginal values of a discounted stochastic game. Further, under mild assumptions on the perturbation, we provide a formula for their limit as the discount rate vanishes and for the marginal values of an undiscounted stochastic game. We also show, via an example, that the two latter differ in general.