On Finding the Leader's Strategy in Quadratic Aggregative Stackelberg Pricing Games

Abstract: This paper analyzes a class of Stackelberg games where different actors compete for shared resources and a central authority tries to balance the demand through a pricing mechanism. Situations like this can for instance occur when fleet owners of electric taxi services compete about charging spots. In this paper, we model the competition between the followers as an aggregative game, i.e., each player's decision only depends on the aggregate strategy of the others. While it has previously been shown that there exist dynamic pricing strategies to achieve the central authority's objective, we in this paper present a method to compute optimal static prices. Proof of convergence of the method is presented, together with a numerical study showcasing the benefits and the speed of convergence of the proposed method.