Abstract
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.
This work was supported by the European Regional Development Fund (ERDF).
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References
Babaioff, M., Kleinberg, R., Papadimitriou, C.H.: Congestion games with malicious players. In: Proc. of the 8th ACM Conf. on Electronic Commerce, pp. 103–112 (2007)
Braess, D.: Über ein Paradoxon der Verkehrsplanung. Unternehmenforschung 11, 258–268 (1968)
Correa, J.R., Schulz, A.S., Stier-Moses, N.E.: Selfish routing in capacitated networks. Mathematics of Operations Research 29, 961–976 (2004)
Correa, J.R., Schulz, A.S., Stier-Moses, N.E.: On the inefficiency of equilibria in congestion games. In: Proc. of the 11th Int. Conf. on Integer Programming and Combinatorial Optimization, pp. 167–181. Springer, Heidelberg (2005)
Correa, J.R., Stier-Moses, N.E.: Stackelberg routing in atomic network games. Technical report, Columbia Business School (February 2007)
Dafermos, S., Sparrow, F.: The traffic assignment problem for a general network. Journal of Research of the National Bureau of Standards, Series B 73, 91–118 (1969)
Dubey, P.: Inefficiency of Nash equilibria. Mathematics of Operations Research 11, 1–8 (1986)
Fotakis, D.: Stackelberg strategies for atomic congestion games. In: Proc. of the 15th European Symp. on Algorithms, pp. 299–310. Springer, Heidelberg (2007)
Harks, T.: Stackelberg strategies and collusion in network games with splittable flow. In: Proc. of the 6th Workshop on Approximation and Online Algorithms (WAOA). Springer, Heidelberg (2008)
Kaporis, A., Spirakis, P.: The price of optimum in Stackelberg games on arbitrary single commodity networks and latency functions. In: Proc. of the 18th ACM Symp. on Parallelism in Algorithms and Architectures, pp. 19–28. ACM Press, New York (2006)
Karakostas, G., Kolliopoulos, S.G.: Stackelberg strategies for selfish routing in general multicommodity networks. Algorithmica (to appear, 2007)
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)
Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. In: Meines, C., Tison, S. (eds.) Proc. of the 16th Symp. on Theoretical Aspects of Computer Science, pp. 404–413. Springer, Heidelberg (1999)
Kumar, V.S.A., Marathe, M.V.: Improved results for Stackelberg scheduling strategies. In: Proc. of the 33rd Int. Colloquium of Automata, Languages and Programming, pp. 776–787. Springer, Heidelberg (2002)
Perakis, G.: The price of anarchy when costs are non-separable and asymmetric. In: Proc. of the 10th Int. Conference on Integer Programming and Combinatorial Optimization, pp. 46–58. Springer, Heidelberg (2004)
Roughgarden, T.: The price of anarchy is independent of the network topology. Journal of Computer and System Sciences 67, 341–364 (2002)
Roughgarden, T.: Selfish Routing. PhD thesis, Cornell University (2002)
Roughgarden, T.: Stackelberg scheduling strategies. SIAM Journal on Computing 33(2), 332–350 (2004)
Roughgarden, T.: Selfish Routing and the Price of Anarchy. MIT Press, Cambridge (2005)
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 (2006)
Roughgarden, T., Tardos, E.: How bad is selfish routing? Journal of the ACM 49(2), 236–259 (2002)
Sharma, Y., Williamson, D.: Stackelberg thresholds in network routing games or the value of altruism. In: Proc. of the 8th ACM Conf. on Electronic Commerce, pp. 93–102 (2007)
Swamy, C.: The effectiveness of Stackelberg strategies and tolls for network congestion games. In: Proc. of the 18th ACM-SIAM Symp. on Discrete Algorithms, pp. 1133–1142. SIAM, Philadelphia (2007)
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Bonifaci, V., Harks, T., Schäfer, G. (2008). Stackelberg Routing in Arbitrary Networks . 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_31
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DOI: https://doi.org/10.1007/978-3-540-92185-1_31
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