A Scalable Solver for 2p0s Differential Games with One-Sided Payoff Information and Continuous Actions, States, and Time

Mukesh Ghimire, Lei Zhang, Zhe Xu, Yi Ren

Abstract: Existing solvers for imperfect-information extensive-form games (IIEFGs) often struggle with scalability in terms of action and state space sizes and the number of time steps. However, many real-world games involve continuous action and state spaces and occur in continuous time, making them differential in nature. This paper addresses the scalability challenges for a representative class of two-player zero-sum (2p0s) differential games where the informed player knows the game type (payoff) while the uninformed one only has a prior belief over the set of possible types. Such games encompass a wide range of attack-defense scenarios, where the defender adapts based on their belief about the attacker's target. We make the following contributions: (1) We show that under the Isaacs' condition, the complexity of computing the Nash equilibrium for these games is not related to the action space size; and (2) we propose a multigrid approach to effectively reduce the cost of these games when many time steps are involved. Code for this work is available at https://github.com/ghimiremukesh/cams/tree/conf_sub.