The Stackelberg Problem: General Case

Abstract

The Stackelberg problem is the most challenging two-level structure that we examine in this book. It has numerous interpretations but originally it was proposed as a model for a leader-follower game in which two players try to minimize their individual objective functions F(x, y) and f (x, y), respectively, subject to a series of interdependent constraints [S28, S27]. Play is defined as sequential and the mood as noncooperative. The decision variables are partitioned between the players in such a way that neither can dominate the other. The leader goes first and through his choice of x ∈ R ⁿ is able to influence but not control the actions of the follower. This is achieved by reducing the set of feasible choices available to the latter. Subsequently, the follower reacts to the leader’s decision by choosing a y ∈ R ^m in an effort to minimizes his costs. In so doing, he indirectly affects the leader’s solution space and outcome.