Stackelberg thresholds on parallel networks with horizontal queues

TitleStackelberg thresholds on parallel networks with horizontal queues
Publication TypeConference Paper
Year of Publication2013
AuthorsJebbari, Y.., W.. Krichene, J.. D. Reilly, and A.. M. Bayen
Conference Name52nd IEEE Conference on Decision and Control
Date PublishedDec
Keywordscompliance 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.