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Article Dans Une Revue Mathematical Programming Année : 2022

Splitting games over finite sets

Résumé

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 first part introduces 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 (Math Oper Res 45:1237–1257, 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.
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Dates et versions

halshs-03672222 , version 1 (21-06-2022)

Identifiants

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Frédéric Koessler, Marie Laclau, Jérôme Renault, Tristan Tomala. Splitting games over finite sets. Mathematical Programming, In press, ⟨10.1007/s10107-022-01806-7⟩. ⟨halshs-03672222⟩
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