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Limit Optimal Trajectories in Zero-Sum Stochastic Games

Author

Listed:
  • Sylvain Sorin

    (Sorbonne Université, UPMC Paris 06)

  • Guillaume Vigeral

    (Université Paris-Dauphine, PSL Research University)

Abstract

We consider zero-sum stochastic games. For every discount factor $$\lambda $$λ, a time normalization allows to represent the discounted game as being played during the interval [0, 1]. We introduce the trajectories of cumulated expected payoff and of cumulated occupation measure on the state space up to time $$t\in [0,1]$$t∈[0,1], under $$\varepsilon $$ε-optimal strategies. A limit optimal trajectory is defined as an accumulation point as ($$\lambda , \varepsilon )$$λ,ε) tend to 0. We study existence, uniqueness and characterization of these limit optimal trajectories for compact absorbing games.

Suggested Citation

  • Sylvain Sorin & Guillaume Vigeral, 2020. "Limit Optimal Trajectories in Zero-Sum Stochastic Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 555-572, June.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:2:d:10.1007_s13235-019-00333-z
    DOI: 10.1007/s13235-019-00333-z
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    References listed on IDEAS

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    1. Jean-François Mertens & Abraham Neyman & Dinah Rosenberg, 2009. "Absorbing Games with Compact Action Spaces," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 257-262, May.
    2. repec:dau:papers:123456789/8023 is not listed on IDEAS
    3. Rida Laraki, 2010. "Explicit formulas for repeated games with absorbing states," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 53-69, March.
    4. Pierre Cardaliaguet & Rida Laraki & Sylvain Sorin, 2012. "A Continuous Time Approach for the Asymptotic Value in Two-Person Zero-Sum Repeated Games," Post-Print hal-00609476, HAL.
    5. MERTENS, Jean-François & ZAMIR, Shmuel, 1971. "The value of two-person zero-sum repeated games with lack of information on both sides," LIDAM Reprints CORE 154, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. repec:dau:papers:123456789/6775 is not listed on IDEAS
    7. Guillaume Vigeral, 2013. "A Zero-Sum Stochastic Game with Compact Action Sets and no Asymptotic Value," Dynamic Games and Applications, Springer, vol. 3(2), pages 172-186, June.
    8. Sylvain Sorin & Guillaume Vigeral, 2013. "Existence of the Limit Value of Two Person Zero-Sum Discounted Repeated Games via Comparison Theorems," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 564-576, May.
    9. repec:dau:papers:123456789/10880 is not listed on IDEAS
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    Cited by:

    1. Miquel Oliu-Barton, 2022. "Weighted-average stochastic games with constant payoff," Operational Research, Springer, vol. 22(3), pages 1675-1696, July.

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