Splitting games over finite sets

• 成果类型: Article
• 署名作者: Koessler, Frederic; Laclau, Marie; Renault, Jerome; Tomala, Tristan
• 署名单位: Paris School of Economics; Centre National de la Recherche Scientifique (CNRS); Hautes Etudes Commerciales (HEC) Paris; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-022-01806-7
• 发表日期: 2024
• 页码: 477-498
• 关键词: pair

摘要

This paper studies zero-sum splitting games with finite sets of states. Players dynamically choose a pair of martingales {p(t) , q(t)}(t), in order to control a terminal payoff u(p(infinity),q(infinity)). 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 epsilon-optimal strategies and we characterize it as the unique concave-convex function satisfying two new conditions.