Abstract
This work studies the price of anarchy and the price of stability of cost-sharing methods in weighted congestion games. We require that our cost-sharing method and our set of cost functions satisfy certain natural conditions and we present general tight price of anarchy bounds, which are robust and apply to general equilibrium concepts. We then turn to the price of stability and prove an upper bound for the Shapley value cost-sharing method, which holds for general sets of cost functions and which is tight in special cases of interest, such as bounded degree polynomials. Also for bounded degree polynomials, we close the paper with a somehow surprising result, showing that a slight deviation from the Shapley value has a huge impact on the price of stability. In fact, for this case, the price of stability becomes as bad as the price of anarchy.
This work was supported by EPSRC grants EP/J019399/1 and EP/L011018/1.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F.: Exact price of anarchy for polynomial congestion games. SIAM Journal on Computing 40(5), 1211–1233 (2011)
Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM Journal on Computing 38(4), 1602–1623 (2008)
Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: Proceedings of STOC, pp. 57–66. ACM (2005)
Bhawalkar, K., Gairing, M., Roughgarden, T.: Weighted congestion games: Price of anarchy, universal worst-case examples, and tightness. ACM Transactions on Economics and Computation 2(4), 14 (2014)
Chen, H.L., Roughgarden, T.: Network design with weighted players. Theory of Computing Systems 45(2), 302–324 (2009)
Chen, H.L., Roughgarden, T., Valiant, G.: Designing network protocols for good equilibria. SIAM Journal on Computing 39(5), 1799–1832 (2010)
Christodoulou, G., Gairing, M.: Price of stability in polynomial congestion games. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 496–507. Springer, Heidelberg (2013)
Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proceedings of STOC, pp. 67–73. ACM (2005)
Gairing, M., Schoppmann, F.: Total latency in singleton congestion games. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 381–387. Springer, Heidelberg (2007)
Gkatzelis, V., Kollias, K., Roughgarden, T.: Optimal cost-sharing in weighted congestion games. In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 72–88. Springer, Heidelberg (2014)
Gopalakrishnan, R., Marden, J.R., Wierman, A.: Potential games are necessary to ensure pure Nash equilibria in cost sharing games. Mathematics of Operations Research (2014)
Harks, T., Klimm, M.: On the existence of pure Nash equilibria in weighted congestion games. Mathematics of Operations Research 37(3), 419–436 (2012)
Klimm, M., Schmand, D.: Sharing non-anonymous costs of multiple resources optimally. In: Paschos, V.T., Widmayer, P. (eds.) CIAC 2015. LNCS, vol. 9079, pp. 274–287. Springer, Heidelberg (2015). arXiv preprint arXiv:1412.4456
Kollias, K., Roughgarden, T.: Restoring pure equilibria to weighted congestion games. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 539–551. Springer, Heidelberg (2011)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. Computer Science Review 3(2), 65–69 (2009)
Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14(1), 124–143 (1996)
Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2(1), 65–67 (1973)
Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: Proceedings of STOC, pp. 513–522. ACM (2009)
Roughgarden, T., Schrijvers, O.: Network cost-sharing without anonymity. In: Lavi, R. (ed.) SAGT 2014. LNCS, vol. 8768, pp. 134–145. Springer, Heidelberg (2014)
Roughgarden, T., Tardos, É.: How bad is selfish routing? Journal of the ACM (JACM) 49(2), 236–259 (2002)
Shapiro, A.: On duality theory of convex semi-infinite programming. Optimization 54(6), 535–543 (2005)
Sheffi, Y.: Urban transportation networks: equilibrium analysis with mathematical programming methods. Prentice-Hall (1985)
Wu, S.Y., Fang, S.C.: Solving convex programs with infinitely many linear constraints by a relaxed cutting plane method. Computers & Mathematics with Applications 38(3), 23–33 (1999)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gairing, M., Kollias, K., Kotsialou, G. (2015). Tight Bounds for Cost-Sharing in Weighted Congestion Games. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47666-6_50
Download citation
DOI: https://doi.org/10.1007/978-3-662-47666-6_50
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-47665-9
Online ISBN: 978-3-662-47666-6
eBook Packages: Computer ScienceComputer Science (R0)