@article{publications45660,
          volume = {vol.203},
           month = {January},
          author = {Fr{\'e}d{\'e}ric Koessler and Marie Laclau and J{\'e}r{\^o}me Renault and Tristan Tomala},
         address = {Heidelberg},
           title = {Splitting games over finite sets},
       publisher = {Springer},
            year = {2024},
         journal = {Mathematical Programming},
           pages = {477--498},
             url = {https://publications.ut-capitole.fr/id/eprint/45660/},
        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{$\infty$},q{$\infty$}). 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 {\ensuremath{\epsilon}}-optimal strategies and we characterize it as the unique concave-convex function satisfying two new conditions.}
}