Abstract

We show exact values for the worst-case price of anarchy in weighted and unweighted (atomic unsplittable) congestion games, provided that all cost functions are bounded-degree polynomials with nonnegative coefficients. The given values also hold for weighted and unweighted network congestion games.

MSC codes

  1. 68Q99
  2. 90B18
  3. 91A10
  4. 91A43

Keywords

  1. atomic unsplittable congestion games
  2. selfish routing
  3. price of anarchy

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References

1.
S. Aland, D. Dumrauf, M. Gairing, B. Monien, and F. Schoppmann, Exact price of anarchy for polynomial congestion games, in Proceedings of the 23rd International Symposium on Theoretical Aspects of Computer Science (STACS'06), Lecture Notes in Comput. Sci. 3884, B. Durand and W. Thomas, eds., Springer, Berlin, 2006, pp. 218–229.
2.
B. Awerbuch, Y. Azar, and A. Epstein, The price of routing unsplittable flow, in Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC'05), ACM Press, 2005, pp. 57–66.
3.
B. Awerbuch, Y. Azar, Y. Richter, and D. Tsur, Tradeoffs in worst-case equilibria, Theoret. Comput. Sci., 361 (2006), pp. 200–209.
4.
M. Beckmann, B. McGuire, and C. Winsten, Studies in the Economics of Transportation, Yale University Press, New Haven, CT, 1956.
5.
K. Bhawalkar, M. Gairing, and T. Roughgarden, Weighted congestion games: Price of anarchy, universal worst-case examples, and tightness, in Proceedings of the 18th Annual European Symposium on Algorithms (ESA'10), Lecture Notes in Comput. Sci. 6347, M. de Berg and U. Meyer, eds., 2010, pp. 17–28.
6.
A. Blum, M. Hajiaghayi, K. Ligett, and A. Roth, Regret minimization and the price of total anarchy, in Proceedings of the 40th Annual ACM Symposium on Theory of Computing (STOC'08), 2008, pp. 373–382.
7.
G. Christodoulou and E. Koutsoupias, On the price of anarchy and stability of correlated equilibria of linear congestion games, in Proceedings of the 13th Annual European Symposium on Algorithms (ESA'05), Lecture Notes in Comput. Sci. 3669, G. Stølting Brodal and S. Leonardi, eds., Springer, Berlin, 2005, pp. 59–70.
8.
G. Christodoulou and E. Koutsoupias, The price of anarchy of finite congestion games, in Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC'05), ACM Press, 2005, pp. 67–73.
9.
R. Cominetti, J. R. Correa, and N. E. Stier-Moses, The impact of oligopolistic competition in networks, Oper. Res., 57 (2009), pp. 1421–1437.
10.
A. Czumaj, P. Krysta, and B. Vöcking, Selfish traffic allocation for server farms, SIAM J. Comput., 39 (2010), pp. 1957–1987.
11.
A. Czumaj and Berthold Vöcking, Tight bounds for worst-case equilibria, ACM Trans. Algorithms, 3 (2007), p. 4.
12.
O. Forster, Analysis 1, 9th ed., Vieweg+Teubner, Wiesbaden, Germany, 2008, pp. 75–81.
13.
D. Fotakis, Congestion games with linearly independent paths: Convergence time and price of anarchy, Theory Comput. Syst., 2009.
14.
D. Fotakis, S. Kontogiannis, and P. Spirakis, Selfish unsplittable flows, Theoret. Comput. Sci., 348 (2005), pp. 226–239.
15.
D. Fotakis, S. Kontogiannis, and P. Spirakis, Symmetry in network congestion games: Pure equilibria and anarchy cost, in Proceedings of the 3rd International Workshop on Approximation and Online Algorithms (WAOA'05), Thomas Erlebach and Giuseppe Persiano, eds., 2005, pp. 161–175.
16.
M. Gairing, T. Lücking, M. Mavronicolas, and B. Monien, The price of anarchy for polynomial social cost, Theoret. Comput. Sci., 369 (2006), pp. 116–135.
17.
M. Gairing, T. Lücking, M. Mavronicolas, and B. Monien, Computing Nash equilibria for scheduling on restricted parallel links, Theory Comput. Syst., 47 (2010), pp. 405–432.
18.
M. Gairing, T. Lücking, M. Mavronicolas, B. Monien, and M. Rode, Nash equilibria in discrete routing games with convex latency functions, J. Comput. Syst. Sci., 74 (2008), pp. 1199–1225.
19.
M. Gairing, T. Lücking, B. Monien, and K. Tiemann, Nash equilibria, the price of anarchy and the fully mixed Nash equilibrium conjecture, in Proceedings of the 32nd International Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 3580, L. Caires et al. eds., Springer, Berlin, 2005, pp. 51–65.
20.
M. Gairing, B. Monien, and K. Tiemann, Selfish routing with incomplete information, Theory Comput. Syst., 42 (2008), pp. 91–130.
21.
M. Gairing and F. Schoppmann, Total latency in singleton congestion games, in Proceedings of the 3rd International Workshop on Internet and Network Economics (WINE'07), Lecture Notes in Comput. Sci. 4858, X. Deng and F. Chung Graham, eds., 2007, pp. 381–387.
22.
T. Harks, Stackelberg strategies and collusion in network games with splittable flow, Theory Comput. Syst., 48 (2011), pp. 781–802.
23.
T. Harks and M. Klimm, On the existence of pure Nash equilibria in weighted congestion games, in Proceedings of the 37th International Colloquium on Automata, Languages, and Programming (ICALP'10), Part I, Lecture Notes in Comput. Sci. 6198, S. Abramsky et al. eds., Springer, Berlin, 2010, pp. 79–89.
24.
E. Koutsoupias, M. Mavronicolas, and P. Spirakis, Approximate equilibria and ball fusion, Theory Comput. Syst., 36 (2003), pp. 683–693.
25.
E. Koutsoupias and C. Papadimitriou, Worst-case equilibria, in Proceedings of the 16th International Symposium on Theoretical Aspects of Computer Science (STACS'99), Lecture Notes in Comput. Sci. 1563, C. Meinel and S. Tison, eds., Springer, Berlin, 1999, pp. 404–413.
26.
L. Libman and A. Orda, Atomic resource sharing in noncooperative networks, Telecommunication Syst., 17 (2001), pp. 385–409.
27.
T. Lücking, M. Mavronicolas, B. Monien, and M. Rode, A new model for selfish routing, Theoret. Comput. Sci., 406 (2008), pp. 187–206.
28.
A. Mas-Colell, M. D. Whinston, and J. R. Green, Microeconomic Theory, Oxford University Press, London, 1995.
29.
I. Milchtaich, Congestion games with player-specific payoff functions, Games and Economic Behavior, 13 (1996), pp. 111–124.
30.
D. Monderer and L. S. Shapley, Potential games, Games and Economic Behavior, 14 (1996), pp. 124–143.
31.
J. F. Nash, Non-cooperative games, Ann. of Math., 54 (1951), pp. 286–295.
32.
C. Papadimitriou, Algorithms, games, and the Internet, in Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC'01), 2001, pp. 749–753.
33.
G. Perakis, The “price of anarchy” under nonlinear and asymmetric costs, Math. Oper. Res., 32 (2007), pp. 614–628.
34.
R. W. Rosenthal, A class of games possessing pure-strategy Nash equilibria, Internat. J. Game Theory, 2 (1973), pp. 65–67.
35.
T. Roughgarden, Selfish Routing and the Price of Anarchy, MIT Press, Cambridge, MA, 2005.
36.
T. Roughgarden, Routing games, in Algorithmic Game Theory, N. Nisan et al. eds., ch. 18, Cambridge University Press, London, 2007.
37.
T. Roughgarden, Intrinsic robustness of the price of anarchy, in Proceedings of the 41st Annual ACM Symposium on Theory of Computing (STOC'09), 2009, pp. 513–522.
38.
T. Roughgarden and F. Schoppmann, Local smoothness and the price of anarchy in atomic splittable congestion games, in Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'11), 2011, pp. 255–267.
39.
T. Roughgarden and É. Tardos, How bad is selfish routing?, J. ACM, 49 (2002), pp. 236–259.
40.
T. Roughgarden and É. Tardos, Bounding the inefficiency of equilibria in nonatomic congestion games, Games and Economic Behavior, 47 (2004), pp. 389–403.
41.
J. G. Wardrop, Some theoretical aspects of road traffic research, in Proceedings of the Institute of Civil Engineers, Part II, 1 (1952), pp. 325–378.
42.
H. Peyton Young, Strategic Learning and its Limits, Oxford University Press, London, 2004.

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Published In

cover image SIAM Journal on Computing
SIAM Journal on Computing
Pages: 1211 - 1233
ISSN (online): 1095-7111

History

Submitted: 9 February 2009
Accepted: 29 April 2011
Published online: 15 September 2011

MSC codes

  1. 68Q99
  2. 90B18
  3. 91A10
  4. 91A43

Keywords

  1. atomic unsplittable congestion games
  2. selfish routing
  3. price of anarchy

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