  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 violate the state constraints if possible, or to maximize the payoff
otherwise. 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 games with state constraints and
the derivation of the primal and dual subdynamic principles necessary for
computing behavioral strategies. Different from existing works that are
concerned about the scalability of no-regret learning in games with discrete
dynamics, our study reveals the underlying structure of strategies for belief
manipulation resulting from information asymmetry and state constraints. This
structure will be necessary for scalable learning on games with continuous
actions and long time windows. 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 deceptive moves
to take advantage of information asymmetry, and compute how the defender should
respond.
