Stackelberg Routing in Arbitrary Networks

  • Vincenzo Bonifaci
  • Tobias Harks
  • Guido Schäfer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5385)


We investigate the impact of Stackelberg routing to reduce the price of anarchy in network routing games. In this setting, an α fraction of the entire demand is first routed centrally according to a predefined Stackelberg strategy and the remaining demand is then routed selfishly by (nonatomic) players. Although several advances have been made recently in proving that Stackelberg routing can in fact significantly reduce the price of anarchy for certain network topologies, the central question of whether this holds true in general is still open. We answer this question negatively. We prove that the price of anarchy achievable via Stackelberg routing can be unbounded even for single-commodity networks. In light of this negative result, we consider bicriteria bounds. We develop an efficiently computable Stackelberg strategy that induces a flow whose cost is at most the cost of an optimal flow with respect to demands scaled by a factor of \(1 + \sqrt{1-\alpha}\). Finally, we analyze the effectiveness of an easy-to-implement Stackelberg strategy, called SCALE. We prove bounds for a general class of latency functions that includes polynomial latency functions as a special case. Our analysis is based on an approach which is simple, yet powerful enough to obtain (almost) tight bounds for SCALE in general networks.


Nash Equilibrium Latency Function Internet Service Provider Congestion Game Scale Strategy 


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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Vincenzo Bonifaci
    • 1
    • 2
  • Tobias Harks
    • 3
  • Guido Schäfer
    • 3
  1. 1.Università degli Studi dell’AquilaItaly
  2. 2.Sapienza Università di RomaItaly
  3. 3.Technische Universität BerlinGermany

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