A minimum sensitivity approach to incentive design problems

In this paper we introduce the notion of "robust" incentive schemes in multi-agent decision problems with a hierarchical decision structure, and discuss derivation of such policies by minimizing, in addition to the usual (standard) Stackelberg performance indices, an appropriate sensitivity function. Such an approach has applications in decision problems wherein the leader does not know the exact values of some parameters characterizing the follower\´s cost functional, and seeks to robustify his optimum policy in the presence of deriations from the nominal values. An in-depth analysis of such incentive design problems is provided, and some concrete analytical results are obtained for general cost functionals with a convex structure. The results are then applied to an incentive design problem arising in economics, leading to some meaningful robust incentive policies.