We study the ergodicity of deterministic two-person zero-sum differential games. This property is defined by the uniform convergence to a constant of either the infinite-horizon discounted value as the discount factor tends to zero, or equivalently, the averaged finite-horizon value as the time goes to infinity. We provide necessary and sufficient conditions for the unique ergodicity of a game. This notion extends the classical one for dynamical systems, namely when ergodicity holds with any (suitable) perturbation of the running payoff function. Our main condition is symmetric between the two players and involve dominions, i.e., subsets of states that one player can make approximately invariant.
A Convergent Algorithm Based on Deterministic Approximation for a Large Class of Regime-Switching Generalized Stochastic Game-Theoretic Riccati Differential Equations
The Simple Strategy-Iteration Method is Strongly Polynomial for the Turn-Based Deterministic Forward Game
Hong Kong University of Science and Technology（香港科技大学）；Stanford University（斯坦福大学）；Shanghai Jiao Tong University（上海交通大学）；Shanghai Institute for Mathematics and Interdisciplinary Sciences（上海数学与交叉学科研究院）
