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A Continuous Time Approach for the Asymptotic Value in Two-Person Zero-Sum Repeated Games

Author

Listed:
  • Pierre Cardaliaguet

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Rida Laraki

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris)

  • Sylvain Sorin

    (X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris, IMJ - Institut de Mathématiques de Jussieu - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider the asymptotic value of two person zero sum repeated games with general evaluations of the stream of stage payoffs. We show existence for incomplete information games, splitting games and absorbing games. The technique of proof consists in embedding the discrete repeated game into a continuous time one and to use viscosity solution tools.

Suggested Citation

  • 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.
    • Handle: RePEc:hal:journl:hal-00609476
    DOI: 10.1137/110839473
    Note: View the original document on HAL open archive server: https://hal.science/hal-00609476
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    References listed on IDEAS

    as
    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    2. Rida Laraki, 2002. "The splitting game and applications," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 359-376.
    3. Rida Laraki, 2002. "Repeated Games with Lack of Information on One Side: The Dual Differential Approach," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 419-440, May.
    4. 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.
    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. Abraham Neyman & Sylvain Sorin, 2010. "Repeated games with public uncertain duration process," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 29-52, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Miquel Oliu-Barton, 2015. "Differential Games with Asymmetric and Correlated Information," Dynamic Games and Applications, Springer, vol. 5(3), pages 378-396, September.
    2. Joseph Abdou & Nikolaos Pnevmatikos, 2016. "Asymptotic value in frequency-dependent games: A differential approach," Documents de travail du Centre d'Economie de la Sorbonne 16076, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Fabien Gensbittel & Jérôme Renault, 2015. "The Value of Markov Chain Games with Incomplete Information on Both Sides," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 820-841, October.
    5. Joseph M. Abdou & Nikolaos Pnevmatikos, 2019. "Asymptotic Value in Frequency-Dependent Games with Separable Payoffs: A Differential Approach," Dynamic Games and Applications, Springer, vol. 9(2), pages 295-313, June.
    6. Pierre Cardaliaguet & Catherine Rainer & Dinah Rosenberg & Nicolas Vieille, 2016. "Markov Games with Frequent Actions and Incomplete Information—The Limit Case," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 49-71, February.
    7. Sylvain Sorin, 2018. "Limit Value of Dynamic Zero-Sum Games with Vanishing Stage Duration," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 51-63, February.
    8. 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.
    9. repec:dau:papers:123456789/10880 is not listed on IDEAS
    10. Miquel Oliu-Barton, 2018. "The Splitting Game: Value and Optimal Strategies," Dynamic Games and Applications, Springer, vol. 8(1), pages 157-179, March.
    11. Fabien Gensbittel, 2015. "Extensions of the Cav( u ) Theorem for Repeated Games with Incomplete Information on One Side," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 80-104, February.
    12. Fabien Gensbittel & Catherine Rainer, 2018. "A Two-Player Zero-sum Game Where Only One Player Observes a Brownian Motion," Dynamic Games and Applications, Springer, vol. 8(2), pages 280-314, June.
    13. 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.
    14. Bruno Ziliotto, 2016. "General limit value in zero-sum stochastic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 353-374, March.

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