Stackelberg Routing on Horizontal Queueing Networks

In order to address inefficiencies of Nash equilibria for horizontal queuing congestion networks, we study the Stackelberg routing game on parallel networks: assuming a coordinator has control over a fraction of the flow, what is a good way of routing that compliant flow so that the induced Nash equilibrium is closer to the social optimum than the initial Nash equilibrium? We study Stackelberg routing for a new class of latency functions, that models congestion on horizontal queuing networks. We show that in this setting, optimal Stackelberg strategies can be computed in polynomial time in the size of the network. We introduce a candidate Stackelberg strategy, the non-compliant first strategy, and prove it to be optimal. We apply these results by modeling a transportation network in which a coordinator can choose the routes of fraction of compliant agents, while the rest of the agents choose their routes selfishly. Some proofs are omitted for brevity, and are available for the reviewer’s convenience in [6].