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2024
- handle: 10670/1.91u1dq
- halshs: halshs-03672222
- doi: 10.1007/s10107-022-01806-7
- WOS: 000791890800001
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info:eu-repo/semantics/altIdentifier/doi/10.1007/s10107-022-01806-7
info:eu-repo/semantics/OpenAccess
Mots-clés
Splitting games Mertens-Zamir system Repeated games with incomplete information Bayesian persuasion Information design MSC: 91A15, 91A27 C - Mathematical and Quantitative Methods/C.C7 - Game Theory and Bargaining Theory/C.C7.C73 - Stochastic and Dynamic Games • Evolutionary Games • Repeated GamesSujets proches
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Frédéric Koessler et al., « Splitting games over finite sets », HAL-SHS : économie et finance, ID : 10.1007/s10107-022-01806-7
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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.