The price of optimum in Stackelberg games on arbitrary single commodity networks and latency functions

  • Authors:

  • A.C. Kaporis;P.G. Spirakis

  • Affiliations:

  • University of Patras, Patras, Greece;University of Patras, Patras, Greece

  • Venue:
  • Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
  • Year:
  • 2006

Quantified Score

Hi-index 0.00

Visualization

Abstract

Let M be a single s-t network of parallel links with load dependent latency functions shared by an infinite number of selfish users. This may yield a Nash equilibrium with unbounded Coordination Ratio [12, 26]. A Leader can decrease the coordination ratio by assigning flow αr on M, and then all Followers assign selfishly the (1 - α)r remaining flow. This is a Stackelberg Scheduling Instance (M,r,α), 0 ≤ α ≤ 1. It was shown [23] that it is weakly NP-hard to compute the optimal Leader's strategy.For any such network M we efficiently compute the minimum portion βM of flow r needed by a Leader to induce M's optimum cost, as well as his optimal strategy.Unfortunately, Stackelberg routing in more general nets can be arbitrarily hard. Roughgarden presented a modification of Braess's Paradox graph, such that no strategy controlling αr flow can induce ≤ 1α times the optimum cost. However, we show that our main result also applies to any s-t net G. We take care of the Braess's graph explicitly, as a convincing example.