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Almost Stationary ∈-Equilibria in Zero-Sum Stochastic Games

Author

Listed:
  • J. Flesch

    (Maastricht University)

  • F. Thuijsman

    (Maastricht University)

  • O. J. Vrieze

    (Maastricht University)

Abstract

We show the existence of almost stationary ∈-equilibria, for all ∈ > 0, in zero-sum stochastic games with finite state and action spaces. These are ∈-equilibria with the property that, if neither player deviates, then stationary strategies are played forever with probability almost 1. The proof is based on the construction of specific stationary strategy pairs, with corresponding rewards equal to the value, which can be supplemented with history-dependent δ-optimal strategies, with small δ > 0, in order to obtain almost stationary ∈-equilibria.

Suggested Citation

  • J. Flesch & F. Thuijsman & O. J. Vrieze, 2000. "Almost Stationary ∈-Equilibria in Zero-Sum Stochastic Games," Journal of Optimization Theory and Applications, Springer, vol. 105(2), pages 371-389, May.
    • Handle: RePEc:spr:joptap:v:105:y:2000:i:2:d:10.1023_a:1004614002737
    DOI: 10.1023/A:1004614002737
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    References listed on IDEAS

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    1. Vrieze, O J & Thuijsman, F, 1989. "On Equilibria in Repeated Games with Absorbing States," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 293-310.
    2. Nicolas Vieille, 1993. "Solvable states in stochastic games," Post-Print hal-00481853, HAL.
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