On the Time Inconsistency Problem of the Robust Leader Strategy

In this paper the problem of the time inconsistency of the leader strategy in a Multi-Model Game is studied. Initially 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. In a previous result the robust Leader-Follower strategy design the min-max strategies for each player which guarantee an equilibrium for the worst case scenario was found. Now this robust strategy are studied in the context of the so called time inconsistency of the leader strategy. We study this problem by means of a doubled extended linear system where the traditional Riccati type equations of the open loop Stackelberg solution are represented by their corresponding co-state equations.