|Title||Stackelberg thresholds on parallel networks with horizontal queues|
|Publication Type||Conference Papers|
|Year of Publication||2013|
|Authors||Jebbari, Y., W. Krichene, J. Reilly, and A. Bayen|
|Conference Name||52nd IEEE Conference on Decision and Control|
|Keywords||compliance rate, game theory, horizontal queues, Lead, Nash equilibrium, network coordinator, network flow, network route, network theory (graphs), parallel networks, queueing theory, Stackelberg routing games, Stackelberg thresholds, system-wide cost function, total travel-time, zero control|
We study Stackelberg routing games on parallel networks with horizontal queues, in which a coordinator (leader) controls a fraction ? of the total flow on the network, and the remaining players (followers) choose their routes selfishly. The objective of the coordinator is to minimize a system-wide cost function, the total travel-time, while anticipating the response of the followers. Nash equilibria of the routing game (with zero control) are known to be inefficient in the sense that the total travel-time is sub-optimal. Increasing the compliance rate ? improves the cost of the equilibrium, and we are interested in particular in the Stackelberg threshold, i.e. the minimal compliance rate that achieves a strict improvement. In this work, we derive the optimal Stackelberg cost as a function of the compliance rate ?, and obtain, in particular, the expression of the Stackelberg threshold.