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Splitting games over finite sets

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  • Koessler, Frédéric
  • Laclau, Marie
  • Renault, Jérôme
  • Tomala, Tristan

Abstract

This paper studies zero-sum splitting games with finite sets of states. Players dynamically choose a pair of martingales {pt,qt}t, in order to control a terminal payoff u(p∞,q∞). A firstpartintroduces the notion of “Mertens-Zamir transform” of a real-valued matrix and use it to approximate the solution of the Mertens-Zamir system for continuous functions on the square [0, 1]2. A second part considers the general case of finite splitting games with arbitrary correspondences containing the Dirac mass on the current state: building on Laraki and Renault (2020), we show that the value exists by constructing non Markovian ε-optimal strategies and we characterize it as the unique concave-convex function satisfying two new conditions.

Suggested Citation

  • Koessler, Frédéric & Laclau, Marie & Renault, Jérôme & Tomala, Tristan, 2022. "Splitting games over finite sets," TSE Working Papers 22-1321, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:126754
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    References listed on IDEAS

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    1. Forges, F., 1984. "Note on Nash equilibria in infinitely repeated games with incomplete information," LIDAM Reprints CORE 573, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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.
    3. MERTENS, Jean-François & ZAMIR, Shmuel, 1977. "A duality theorem on a pair of simultaneous functional equations," LIDAM Reprints CORE 321, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. 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).
    5. Rida Laraki & Jérôme Renault, 2020. "Acyclic Gambling Games," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1237-1257, November.
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