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Marginal Values of a Stochastic Game

Author

Listed:
  • Luc Attia

    (Université Paris-Dauphine, Paris Sciences and Lettres Research University, Centre National de la Recherche Scientifique, Centre de Recherche en Mathématiques de la Décision, 75775 Paris, France)

  • Miquel Oliu-Barton

    (Université Paris-Dauphine, Paris Sciences and Lettres Research University, Centre National de la Recherche Scientifique, Centre de Recherche en Mathématiques de la Décision, 75775 Paris, France)

  • Raimundo Saona

    (Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria)

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.

Suggested Citation

  • Luc Attia & Miquel Oliu-Barton & Raimundo Saona, 2025. "Marginal Values of a Stochastic Game," Mathematics of Operations Research, INFORMS, vol. 50(1), pages 482-505, February.
    • Handle: RePEc:inm:ormoor:v:50:y:2025:i:1:p:482-505
    DOI: 10.1287/moor.2023.0297
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