On Linear Convergence for Stackelberg Aggregative Games

This article proposes a hierarchical leader–follower game, called Stackelberg aggregative games, with the consideration of an aggregative variable determined by all the players over a multiagent network. In this problem, a leader makes its decision first, followed by the followers in response to the leader’s decision. Each follower aims to minimize its individual cost, which is determined by its own strategy, the leader’s strategy, and the aggregative strategy of all the followers, through local information communication over the network. Similarly, the leader’s cost depends on its own strategy and the aggregative strategy of all the followers. A distributed algorithm is proposed based on projection descent method, which is shown to converge to the Stackelberg equilibrium at a linear rate under the strongly monotone assumption. A numerical experiment on lane merge scenario is provided to validate the theoretical result.