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Computing uniformly optimal strategies in two-player stochastic games

Author

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  • Eilon Solan

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  • Nicolas Vieille

    ()

Abstract

We provide a computable algorithm to calculate uniform ε-optimal strategies in two-player zero-sum stochastic games. Our approach can be used to construct algorithms that calculate uniform ε-equilibria and uniform correlated ε-equilibria in various classes of multi-player non-zero-sum stochastic games.
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Suggested Citation

  • Eilon Solan & Nicolas Vieille, 2010. "Computing uniformly optimal strategies in two-player stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 237-253, January.
  • Handle: RePEc:spr:joecth:v:42:y:2010:i:1:p:237-253
    DOI: 10.1007/s00199-009-0437-1
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    File URL: http://hdl.handle.net/10.1007/s00199-009-0437-1
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    References listed on IDEAS

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    2. 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.
    3. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    4. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832 Elsevier.
    5. Eilon Solan & Nicolas Vieille, 2001. "Quitting Games," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 265-285, May.
    6. Eilon Solan & Nicolas Vieille, 2002. "Perturbed Markov Chains," Discussion Papers 1342, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Vrieze, O.J. & Tijs, S.H., 1982. "Fictitious play applied to sequences of games and discounted stochastic games," Other publications TiSEM da21d287-bc00-4a8e-a18f-0, Tilburg University, School of Economics and Management.
    8. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
    9. Abraham Neyman, 2002. "Stochastic games: Existence of the MinMax," Discussion Paper Series dp295, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    10. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, March.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, March.
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    Citations

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    Cited by:

    1. Bernhard Stengel, 2010. "Computation of Nash equilibria in finite games: introduction to the symposium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 1-7, January.
    2. Miquel Oliu-Barton, 2012. "The asymptotic value in finite stochastic games," Working Papers halshs-00772631, HAL.
    3. Cheng, Jianqiang & Leung, Janny & Lisser, Abdel, 2016. "Random-payoff two-person zero-sum game with joint chance constraints," European Journal of Operational Research, Elsevier, vol. 252(1), pages 213-219.
    4. Chandrasekher, Madhav, 2015. "Unraveling in a repeated moral hazard model with multiple agents," Theoretical Economics, Econometric Society, vol. 10(1), January.

    More about this item

    Keywords

    Optimal strategies; Stochastic games; Computation; C63; C73;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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