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∞,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.
Replaces
Frédéric Koessler, Marie Laclau, Jérôme Renault, and Tristan Tomala, “Splitting games over finite sets”, TSE Working Paper, n. 22-1321, March 2022.
Reference
Frédéric Koessler, Marie Laclau, Jérôme Renault, and Tristan Tomala, “Splitting games over finite sets”, Mathematical Programming, n. 53, 2022.
See also
Published in
Mathematical Programming, n. 53, 2022