Stackelberg Routing in Arbitrary Networks

  • Authors:
  • Vincenzo Bonifaci;Tobias Harks;Guido Schäfer

  • Affiliations:
  • Università degli Studi dell'Aquila, Italy and Sapienza Università di Roma, Italy;Technische Universität Berlin, Germany;Technische Universität Berlin, Germany

  • Venue:
  • WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
  • Year:
  • 2008

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Abstract

We investigate the impact of Stackelberg routing to reduce theprice of anarchy in network routing games. In this setting, anα fraction of the entire demand is first routed centrallyaccording to a predefined Stackelberg strategy and the remainingdemand is then routed selfishly by (nonatomic) players. Althoughseveral advances have been made recently in proving thatStackelberg routing can in fact significantly reduce the price ofanarchy for certain network topologies, the central question ofwhether this holds true in general is still open. We answer thisquestion negatively. We prove that the price of anarchy achievablevia Stackelberg routing can be unbounded even for single-commoditynetworks. In light of this negative result, we consider bicriteriabounds. We develop an efficiently computable Stackelberg strategythat induces a flow whose cost is at most the cost of an optimalflow with respect to demands scaled by a factor of $1 +\sqrt{1-\alpha}$. Finally, we analyze the effectiveness of aneasy-to-implement Stackelberg strategy, called SCALE. We provebounds for a general class of latency functions that includespolynomial latency functions as a special case. Our analysis isbased on an approach which is simple, yet powerful enough to obtain(almost) tight bounds for SCALE in general networks. This work wassupported by the European Regional Development Fund (ERDF).