Stackelberg Strategies and Incentives in Multiperson Deterministic Decision Problems

In this paper discrete and continuous-time two-person decision problems with a hierarchical decision structure are studied and applicability and appropriateness of a function—space approach in the derivation of causal real-time implementable optimal Stackelberg (incentive) strategies under various information patterns are discussed. Results on existence and derivation of incentive strategies for dynamic games formulated in abstract inner-product spaces, in the absence of any causality restriction on the leader's policies, are first presented and then these results are extended (and specialized) in two major directions: 1) discrete-time dynamic games with informational advantage to the leader at each stage of the decision process, which involves partial observation of the follower's decisions; and derivation of multistage incentive strategies for the leader under a feedback Stackelberg solution adapted to the feedback information pattern; and 2) derivation of causal, physically realizable optimum affine Stackelberg policies for both discrete and continuous-time problems, in terms of the gradients of the cost functionals evaluated at the optimum (achievable) operating point (which is in some cases the globally minimizing solution of the leader's cost functional). The paper is concluded with some applications of the theory to important special cases, some extensions to infinite-horizon problems, and some numerical examples that further illustrate these results.