Leader-follower strategies for a multi-plant differential game

Abstract

In this paper the formulation of a concept for a type of robust leader-follower equilibrium for a multi-plant or multiple scenarios differential game is developed. The game dynamic is given by a family of N different possible differential equations (multi-model representation) with no information about the trajectory which is realized. The robust leader-follower strategy for each player must confront with all possible scenarios simultaneously. The problem of each player is the designing of min-max strategies for each player which guarantee an equilibrium for the worst case scenario. Based on the robust maximum principle, the conditions for a game to be in robust leader-follower equilibrium are presented. As in the Nash equilibrium case the initial min-max differential game may be converted into a standard static game given in a multidimensional simplex. A numerical procedure for resolving the case of linear quadratic differential game is presented.