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.

翻译：本文研究了具有状态约束和单边信息的零和微分博弈，其中知情博弈方（玩家1）拥有非知情博弈方（玩家2）未知的离散收益类型。玩家1的目标是在不违反约束的前提下最小化其收益，而玩家2的目标是违反状态约束，或反之最大化收益。该博弈的一个实例是足球比赛中的一对一对抗。在无状态约束的情形下，Cardaliaguet (2007) 证明了此类博弈的值存在且关于博弈方的共同信念是凸的。本文的理论贡献在于将该结果推广至含状态约束的微分博弈，并推导了计算行为策略所必需的原始和对偶子动态原理。与现有聚焦于可扩展性和泛化性的非完美信息动态博弈研究不同，本文重点揭示了由信息不对称和状态约束导致的信念操纵行为机制。我们通过一个简化足球博弈验证了本工作的实用性：揭示了攻击方应（或不应）利用信息不对称实施特定随机假动作的球员位置与信念状态，并计算了防守方应如何应对。