Splitting games over finite sets.

Summary This paper studies zero-sum splitting games with finite sets of posterior beliefs. Players dynamically choose a pair {p t , q t } t of martingales of posteriors in order to control a terminal payoff u(p ∞ , q ∞). We introduce the notion of "Mertens-Zamir transform" of a real-valued matrix and use it to approximate the solution of the Mertens-Zamir system in the unidimensional continuous case. Then, we consider the general case of splitting games with arbitrary contraints and finite sets of posterior beliefs: 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.