State-Constrained Zero-Sum Differential Games with One-Sided Information
Mukesh Ghimire Lei Zhang Zhe Xu Yi Ren
We study zero-sum differential games with state constraints and one-sided
information, where the informed player (Player 1) has a categorical payoff type
unknown to the uninformed player (Player 2). The goal of Player 1 is to
minimize his payoff without violating the constraints, while that of Player 2
is to either violate the state constraints, or otherwise, to maximize the
payoff. One example of the game is a man-to-man matchup in football. Without
state constraints, Cardaliaguet (2007) showed that the value of such a game
exists and is convex to the common belief of players. Our theoretical
contribution is an extension of this result to differential games with state
constraints and the derivation of the primal and dual subdynamic principles
necessary for computing the behavioral strategies. Compared with existing works
on imperfect-information dynamic games that focus on scalability and
generalization, our focus is instead on revealing the mechanism of belief
manipulation behaviors resulted from information asymmetry and state
constraints. We use a simplified football game to demonstrate the utility of
this work, where we reveal player positions and belief states in which the
attacker should (or should not) play specific random fake moves to take
advantage of information asymmetry, and compute how the defender should
respond.