Incentive stackelberg strategies for deterministic multi-stage decision processes

In this paper, we formulate a general incentive Stackelberg dynamic game problem with informational advantage to the leader at each stage of the decision process, which involves partial observation of the follower's decisions. Under a feedback Stackelberg solution concept adapted to this information pattern, some general results on the existence and construction of optimal incentive strategies are obtained, and the derivation of optimal affine policies is discussed. The paper also deals with the global Stackelberg solution in discrete and continuous-time games, and obtains conditions for the existence of causal, physically realizable solutions, in terms of the gradients of the cost functionals evaluated at the optimum operating point.