Differential Games: A Viability Approach

The usual intertemporal optimality criterion traditionally used in differential games is replaced here by a myopic criterion, playability, which requires that at each instant, the state of the game obeys playability constraints. (For simplicity, only time-independent playability constraints are presented below.) Game theoretical concepts are adapted to this case and characterized through conveniently generalized Isaacs’ equations, the contingent Isaacs’ inequalities. For each of these concepts, feedback controls are constructed, according to several game theoretical selection procedures when they are not uniquely determined by contingent Isaacs’ inequalities. The question of choosing strategies through their velocities regarded as decisions is also investigated, and decision rules allowing victory or defeat are characterized through other contingent partial differential equations