Abstract
We study taxes in the well-known game theoretic traffic model due to Wardrop. Given a network and a subset of edges, on which we can impose taxes, the problem is to find taxes inducing an equilibrium flow of minimal network-wide latency cost. If all edges are taxable, then marginal cost pricing is known to induce the socially optimal flow for arbitrary multi-commodity networks. In contrast, if only a strict subset of edges is taxable, we show NP-hardness of finding optimal taxes for general networks with linear latency functions and two commodities. On the positive side, for single-commodity networks with parallel links and linear latency function, we provide a polynomial time algorithm for finding optimal taxes.
Supported by the DFG GK/1298 “AlgoSyn” and by the German Israeli Foundation (GIF) under contract 877/05.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Beckmann, M., McGuire, C.B., Winston, C.B.: Studies in the Economics of Transportation. Yale University Press (1956)
Braess, D.: Über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung 12, 258–268 (1968)
Cocchi, R., Shenker, S., Estrin, D., Zhang, L.: Pricing in computer networks: motivation, formulation, and example. IEEE/ACM Transactions on Networking 1(6), 614–627 (1993)
Cole, R., Dodis, Y., Roughgarden, T.: How much can taxes help selfish routing? In: Proc. 4th EC, pp. 98–107 (2003)
Cole, R., Dodis, Y., Roughgarden, T.: Pricing edges for heterogeneous selfish users. In: Proc. 35th STOC, pp. 521–530 (2003)
Dafermos, S., Sparrow, F.T.: The Traffic Assignment Problem for a General Network. Journal of Research of the National Bureau of Standards, Series B 73(2), 91–118 (1969)
Fleischer, L.: Linear tolls suffice: New bounds and algorithms for tolls in single source networks. Theoretical Computer Science 348, 217–225 (2005)
Fleischer, L., Jain, K., Mahdian, M.: Taxes for heterogeneous selfish users in a multicommodity network. In: Proc. 45th FOCS, pp. 277–285 (2004)
Kaporis, A.C., Spirakis, P.G.: The price of optimum in stackelberg games on arbitrary single commodity networks and latency function. In: Proc. 18th SPAA (2006)
Karakostas, G., Kolliopoulos, S.G.: Edge pricing of multicommodity networks for heterogeneous selfish users. In: Proc. 45th FOCS, pp. 268–276 (2004)
Karakostas, G., Kolliopoulos, S.G.: Stackelberg strategies for selfish routing in general multicommodity networks. Algorithmica (to appear, 2008)
Korilis, Y.A., Lazar, A.A., Orda, A.: Achieving network optima using Stackelberg routing strategies. IEEE/ACM Transactions on Networking 5(1), 161–173 (1997)
Korilis, Y.A., Lazar, A.A., Orda, A.: Capacity allocation under noncooperative routing. IEEE Transactions on Automatic Control 42, 309–325 (1997)
Koutsoupias, E., Papadimitriou, C.: Worst-Case Equilibria. In: Proc. 16th STACS, pp. 404–413 (1999)
Kumar, V.S.A., Marathe, A.: Improved results for Stackelberg scheduling strategies. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380. Springer, Heidelberg (2002)
Pigou, A.C.: The Economics of Welfare. Macmillan, Basingstoke (1920)
Roughgarden, T.: Stackelberg scheduling strategies. In: Proc. 33rd STOC, pp. 104–113 (2001)
Roughgarden, T.: The Price of Anarchy is Independent of the Network Topology. In: Proc. 34th STOC, pp. 428–437 (2002)
Roughgarden, T., Tardos, É.: How Bad is Selfish Routing? Journal of the ACM 49(2), 236–259 (2002)
Roughgarden, T.: On the Severity of Braess’s Paradox: Designing Networks for Selfish Users is Hard. Journal of Computer and System Sciences 72(5), 922–953 (2004)
Roughgarden, T.: Selfish Routing and the Price of Anarchy. MIT Press, Cambridge (2005)
Sharma, Y., Williamson, D.P.: Stackelberg thresholds in network routing games or the value of altruism. In: Proc. 8th EC, pp. 93–102 (2007)
Swamy, C.: The effectiveness of Stackelberg strategies and tolls for network congestion games. In: Proc. 18th SODA, pp. 1133–1142 (2007)
Wardrop, J.G.: Some Theoretical Aspects of Road Traffic Research. In: Proc. of the Institute of Civil Engineers, Pt. II, pp. 325–378 (1952)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hoefer, M., Olbrich, L., Skopalik, A. (2008). Taxing Subnetworks. In: Papadimitriou, C., Zhang, S. (eds) Internet and Network Economics. WINE 2008. Lecture Notes in Computer Science, vol 5385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92185-1_35
Download citation
DOI: https://doi.org/10.1007/978-3-540-92185-1_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92184-4
Online ISBN: 978-3-540-92185-1
eBook Packages: Computer ScienceComputer Science (R0)