Marginal values of a stochastic game

Attia L, Oliu-Barton M, Saona Urmeneta RJ. 2024. Marginal values of a stochastic game. Mathematics of Operations Research.

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Journal Article | Epub ahead of print | English
Author
Attia, Luc; Oliu-Barton, Miquel; Saona, RaimundoISTA
Abstract
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.
Publishing Year
Date Published
2024-03-12
Journal Title
Mathematics of Operations Research
Acknowledgement
This work was supported by Fondation CFM pour la Recherche; the European Research Council [Grant ERC-CoG-863818 (ForM-SMArt)]; and Agence Nationale de la Recherche [Grant ANR-21-CE40-0020].
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Attia L, Oliu-Barton M, Saona Urmeneta RJ. Marginal values of a stochastic game. Mathematics of Operations Research. 2024. doi:10.1287/moor.2023.0297
Attia, L., Oliu-Barton, M., & Saona Urmeneta, R. J. (2024). Marginal values of a stochastic game. Mathematics of Operations Research. Institute for Operations Research and the Management Sciences. https://doi.org/10.1287/moor.2023.0297
Attia, Luc, Miquel Oliu-Barton, and Raimundo J Saona Urmeneta. “Marginal Values of a Stochastic Game.” Mathematics of Operations Research. Institute for Operations Research and the Management Sciences, 2024. https://doi.org/10.1287/moor.2023.0297.
L. Attia, M. Oliu-Barton, and R. J. Saona Urmeneta, “Marginal values of a stochastic game,” Mathematics of Operations Research. Institute for Operations Research and the Management Sciences, 2024.
Attia L, Oliu-Barton M, Saona Urmeneta RJ. 2024. Marginal values of a stochastic game. Mathematics of Operations Research.
Attia, Luc, et al. “Marginal Values of a Stochastic Game.” Mathematics of Operations Research, Institute for Operations Research and the Management Sciences, 2024, doi:10.1287/moor.2023.0297.

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