Efficiency of Restricted Tolls in Non-atomic Network Routing Games
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An effective means to reduce the inefficiency of Nash flows in non-atomic network routing games is to impose tolls on the arcs of the network. It is a well-known fact that marginal cost tolls induce a Nash flow that corresponds to a minimum cost flow. However, despite their effectiveness, marginal cost tolls suffer from two major drawbacks, namely (i) that potentially every arc of the network is tolled, and (ii) that the imposed tolls can be arbitrarily large.
In this paper, we study the restricted network toll problem in which tolls can be imposed on the arcs of the network but are restricted to not exceed a predefined threshold for every arc. We show that optimal restricted tolls can be computed efficiently for parallel-arc networks and affine latency functions. This generalizes a previous work on taxing subnetworks to arbitrary restrictions. Our algorithm is quite simple, but relies on solving several convex programs. The key to our approach is a characterization of the flows that are inducible by restricted tolls for single-commodity networks. We also derive bounds on the efficiency of restricted tolls for multi-commodity networks and polynomial latency functions. These bounds are tight even for parallel-arc networks. Our bounds show that restricted tolls can significantly reduce the price of anarchy if the restrictions imposed on arcs with high-degree polynomials are not too severe. Our proof is constructive. We define tolls respecting the given thresholds and show that these tolls lead to a reduced price of anarchy by using a (λ,μ)-smoothness approach.
KeywordsMinimum Cost Latency Function Threshold Function Congestion Game Optimal Toll
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- 1.Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: Proc. 37th ACM Symp. on Theory of Computing, pp. 57–66 (2005)Google Scholar
- 2.Beckmann, M., McGuire, B., Winsten, C.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)Google Scholar
- 4.Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proc. 37th ACM Symp. on Theory of Computing (2005)Google Scholar
- 5.Christodoulou, G., Koutsoupias, E., Spirakis, P.G.: On the performance of approximate equilibria in congestion games. In: Proc. 17th European Symp. on Algorithms, pp. 251–262 (2009)Google Scholar
- 6.Cole, R., Dodis, Y., Roughgarden, T.: Pricing network edges for heterogeneous selfish users. In: Proc. 35th Symp. on Theory of Computing, pp. 521–530 (2003)Google Scholar
- 9.Fleischer, L., Jain, K., Mahdian, M.: Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games. In: Proc. 45th Symp. on Foundations of Computer Science, pp. 277–285 (2004)Google Scholar
- 11.Harks, T., Schäfer, G., Sieg, M.: Computing flow-inducing network tolls. Technical Report 36-2008, Institut für Mathematik, Technische Universität Berlin, Germany (2008)Google Scholar
- 13.Karakostas, G., Kolliopoulos, S.G.: Edge pricing of multicommodity networks for heterogeneous selfish users. In: Proc. 45th Symp. on Foundations of Computer Science, pp. 268–276 (2004)Google Scholar
- 14.Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. In: Proc. 16th Symp. on Theoretical Aspects of Computer Science, pp. 404–413 (1999)Google Scholar
- 18.Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: Proc. 41st ACM Symp. on Theory of Computing, pp. 513–522 (2009)Google Scholar
- 20.Swamy, C.: The effectiveness of Stackelberg strategies and tolls for network congestion games. In: Proc. 18th Symp. on Discrete Algorithms (2007)Google Scholar