In this bibliography main directions of research as well as main fields of applications of bilevel programming problems and mathematical programs with equilibrium constraints are summarized. Focus is also on the difficulties arising from nonuniqueness of lower-level optimal solutions and on optimality conditions.

Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints

A cooperative incentive equilibrium for a resource management problem

Discrete and continuous-time two-person decision problems with a hierarchical decision structure are studied, and the 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 presented; these results are extended and specialized in two major directions: (1) discrete-time dynamic games, and (2) derivation of causal, physically realizable optimum affine Stackelberg policies for both discrete and continuous-time problems.

Stackelberg strategies and incentives in multiperson deterministic decision problems

The construction of time-lag incentive strategies for continuous time convex problems is considered. The strategies are affine in the data available and they are represented by means of Stieltjes measures. It is shown how incentive strategies can be used as equilibrium strategies in symmetric games where the decision makers are cooperative.

Incentive strategies and equilibria for dynamic games with delayed information

Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography

Through a geometric approach, it is shown that a sufficiently large class of incentive (Stackelberg) problems with perfect or partial dynamic information admits optimal incentive schemes that are affine in the available information. As a byproduct of the analysis, explicit expressions for these affine incentive schemes are obtained, and the general results are applied to two different classes of Stackelberg game problems with partial dynamic information.

Ying-Ping Zheng

Papers

Existence and derivation of optimal affine incentive schemes for Stackelberg games with partial information: a geometric approach†