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Optimal Strategies in Zero-Sum Repeated Games with Incomplete Information: The Dependent Case

Author

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  • Fabien Gensbittel

    (Toulouse School of Economics, University of Toulouse Capitole)

  • Miquel Oliu-Barton

    (Université Paris-Dauphine, PSL Research University, CNRS, CEREMADE)

Abstract

Using the duality techniques introduced by De Meyer (Math Oper Res 21:209–236, 1996a, Math Oper Res 21:237–251, 1996b), Rosenberg (Int J Game Theory 27:577–597, 1998) and De Meyer and Marino (Cahiers de la MSE 27, 2005) provided an explicit construction for optimal strategies in repeated games with incomplete information on both sides, in the independent case. In this note, we extend both the duality techniques and the construction of optimal strategies to the dependent case.

Suggested Citation

  • Fabien Gensbittel & Miquel Oliu-Barton, 2020. "Optimal Strategies in Zero-Sum Repeated Games with Incomplete Information: The Dependent Case," Dynamic Games and Applications, Springer, vol. 10(4), pages 819-835, December.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:4:d:10.1007_s13235-020-00347-y
    DOI: 10.1007/s13235-020-00347-y
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    References listed on IDEAS

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    1. Bernard De Meyer, 1996. "Repeated Games, Duality and the Central Limit Theorem," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 237-251, February.
    2. Miquel Oliu-Barton, 2015. "Differential Games with Asymmetric and Correlated Information," Dynamic Games and Applications, Springer, vol. 5(3), pages 378-396, September.
    3. Miquel Oliu-Barton, 2018. "The Splitting Game: Value and Optimal Strategies," Dynamic Games and Applications, Springer, vol. 8(1), pages 157-179, March.
    4. De Meyer, B., 1996. "Repeated games and partial differential equations," LIDAM Reprints CORE 1209, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. De Meyer, B., 1996. "Repeated games, duality and the central limit theorem," LIDAM Reprints CORE 1210, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. DE MEYER , Bernard, 1993. "Repeated Games and the Central Limit Theorem," LIDAM Discussion Papers CORE 1993003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Heuer, M, 1992. "Asymptotically Optimal Strategies in Repeated Games with Incomplete Information," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 377-392.
    8. Bernard De Meyer & Alexandre Marino, 2005. "Duality and optimal strategies in the finitely repeated zero-sum games with incomplete information on both sides," Cahiers de la Maison des Sciences Economiques b05027, Université Panthéon-Sorbonne (Paris 1).
    9. Bernard de Meyer, 1996. "Repeated games, Duality, and the Central Limit Theorem," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00259714, HAL.
    10. Bernard de Meyer, 1996. "Repeated games, Duality, and the Central Limit Theorem," Post-Print hal-00259714, HAL.
    11. Bernard de Meyer, 1996. "Repeated games and Partial Differential Equations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00259711, HAL.
    12. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    13. Dinah Rosenberg, 1998. "Duality and markovian strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 577-597.
    14. Bernard de Meyer, 1996. "Repeated games and Partial Differential Equations," Post-Print hal-00259711, HAL.
    15. 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).
    16. Bernard De Meyer, 1996. "Repeated Games and Partial Differential Equations," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 209-236, February.
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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. Chen, Fang & Guo, Xianping, 2023. "Two-person zero-sum risk-sensitive stochastic games with incomplete reward information on one side," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 218-245.

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