Two-layer piecewise deterministic games

Equilibrium solutions are characterized for a class of two-layer differential games in which one player, P₂, controls a continuous-time deterministic system while another player, P ₁, intervenes only at random stopping times when he or she can impulsively modify the state and the mode of the lower layer system. They explore the case in which the objectives of the two layers do not coincide totally. This model is also related to the theory of piecewise deterministic systems. Equilibria can be defined and characterized by reformulating this differential game as a noncooperative sequential Markov game with continuous state and action spaces. A precise definition of this class of systems is given and a reformulation in a sequential game format is presented. An existence proof for ε-equilibria and a computational approach are presented