%0 Journal Article
%@ 0025-5610
%A Koessler, Frédéric
%A Laclau, Marie
%A Renault, Jérôme
%A Tomala, Tristan
%C Heidelberg
%D 2024
%F publications:45660
%I Springer
%J Mathematical Programming
%P 477-498
%R 10.1007/s10107-022-01806-7
%T Splitting games over finite sets
%U https://publications.ut-capitole.fr/id/eprint/45660/
%V vol.203
%X 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.