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The splitting game and applications

Author

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  • Rida Laraki

    (CNRS and Laboratoire d'Econométrie de l'Ecole Polytechnique, 1 rue Descartes, 75005 Paris, France. Revised November 2001)

Abstract

First we define the splitting operator, which is related to the Shapley operator of the splitting game introduced by Sorin (2002). It depends on two compact convex sets C and D and associates to a function defined on C ×D a saddle function, extending the usual convexification or concavification operators. We first prove general properties on its domain and its range. Then we give conditions on C and D allowing to preserve continuity or Lipschitz properties, extending the results in Laraki (2001a) obtained for the convexification operator. These results are finally used, through the analysis of the asymptotic behavior of the splitting game, to prove the existence of a continuous solution for the Mertens-Zamir system of functional equations (Mertens and Zamir (1971-72) and (1977)) in a quite general framework.

Suggested Citation

  • Rida Laraki, 2002. "The splitting game and applications," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 359-376.
    • Handle: RePEc:spr:jogath:v:30:y:2002:i:3:p:359-376
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    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. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Koessler, Frederic & Laclau, Marie & Renault, Jérôme & Tomala, Tristan, 2022. "Long information design," Theoretical Economics, Econometric Society, vol. 17(2), May.
    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. Tomala, Tristan & Koessler, Frederic & Laclau, Marie, 2018. "Interactive Information Design," HEC Research Papers Series 1260, HEC Paris, revised 02 May 2018.
    6. 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.
    7. Miquel Oliu-Barton, 2018. "The Splitting Game: Value and Optimal Strategies," Dynamic Games and Applications, Springer, vol. 8(1), pages 157-179, March.
    8. Sylvain Sorin, 2011. "Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 172-207, March.
    9. 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.
    10. Rida Laraki & Jérôme Renault, 2020. "Acyclic Gambling Games," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1237-1257, November.

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