Abstract
We study economic means to improve network performance in the well-known game theoretic traffic model due to Wardrop. We introduce two sorts of spam flow - auxiliary and adversarial flow - that have no intrinsic value. Auxiliary/adversarial flows are a separate commodity with the sole objective to minimize/maximize the latency at the induced Wardrop equilibrium of the selfish flow. By this means a separate access to the edges is not necessary and the latency of the regulating flow does not distort the arising latency cost. We present networks where auxiliary flow is able to improve the network performance. However, we show that the optimal auxiliary flow is NP-hard to compute and not approximable within a factor of less then \(\frac 43\). The minimal amount of auxiliary flow needed to induce the best possible equilibrium is even hard to approximate by any subexponential factor. These hardness results are complemented by proving NP-hardness for the optimal adversarial flow. All hardness results hold even for single-commodity networks.
Supported by the DFG GK/1298 “AlgoSyn”, by the German Israeli Foundation (GIF) under contract 877/05, and by DFG through UMIC Research Centre at RWTH Aachen University.
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References
Babaioff, M., Kleinberg, R., Papadimitriou, C.: Congestion games with malicious players. In: Proc. 8th EC, pp. 103–112 (2007)
Beckmann, M., McGuire, C.B., Winston, C.B.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)
Braess, D.: Über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung 12, 258–268 (1968)
Bonifaci, V., Harks, T., Schäfer, G.: Stackelberg routing in arbitrary networks. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 239–250. Springer, Heidelberg (2008)
Chen, P., Kempe, D.: Altruism, selfishness, and spite in traffic routing. In: Proc. 9th EC, pp. 140–149 (2008)
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. J. Research 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)
Fortune, S., Hopcroft, J.E., Wyllie, J.: The Directed Subgraph Homeomorphism Problem. Theoretical Computer Science 10, 111–121 (1980)
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, p. 776. Springer, Heidelberg (2002)
Pigou, A.C.: The Economics of Welfare. Macmillan, Basingstoke (1920)
Roth, A.: The Price of Malice in Linear Congestion Games. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 118–125. Springer, Heidelberg (2008)
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? J. ACM 49(2), 236–259 (2002)
Roughgarden, T.: On the Severity of Braess’s Paradox: Designing Networks for Selfish Users is Hard. JCSS 72(5), 922–953 (2006)
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)
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Hoefer, M., Olbrich, L., Skopalik, A. (2009). Doing Good with Spam Is Hard. In: Mavronicolas, M., Papadopoulou, V.G. (eds) Algorithmic Game Theory. SAGT 2009. Lecture Notes in Computer Science, vol 5814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04645-2_24
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