Splitting games over finite sets.

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 ∞ , 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. [ABSTRACT FROM AUTHOR]