Network Stackelberg Games and Mathematical Programs with Equilibrium Constraints

Abstract

In this chapter we are concerned with the problem known as a mathematical program with equilibrium constraints (MPEC) and with its game theoretic counterpart – the Stackelberg game . MPECs and Stackelberg games arise in many branches of engineering, science, and economics. MPEC network applications include certain network design , plant location , congestion pricing, and tolling problems formulated so that a fixed-point, nonlinear complementarity, variational inequality, or other mathematical representation of an equilibrium acts as a set of constraints on the optimizing intentions of a central authority. In particular, an MPEC is based on a partition of decision variables into two sets: those variables that are directly determined by a “leader” or omniscient agent, and those variables that are determined by a noncooperative Nash game among so-called “followers” who take the leader’s strategy as given. That is, the leader’s actions are beyond the followers’ influence.