Abstract
The price of anarchy (PoA) in congestion games has attracted a lot of research over the past decade. This has resulted in a thorough understanding of this concept. In contrast, the price of stability (PoS), which is an equally interesting concept, is much less understood.
In this article, we consider congestion games with polynomial cost functions with nonnegative coefficients and maximum degree d. We give matching bounds for the PoS in such games—that is, our technique provides the exact value for any degree d.
For linear congestion games, tight bounds were previously known. Those bounds hold even for the more restricted case of dominant equilibria, which may not exist. We give a separation result showing that this is not possible for congestion games with quadratic cost functions—in other words, the PoA for the subclass of games that admit a dominant strategy equilibrium is strictly smaller than the PoS for the general class.
- Sebastian Aland, Dominic Dumrauf, Martin Gairing, Burkhard Monien, and Florian Schoppmann. 2011. Exact price of anarchy for polynomial congestion games. SIAM Journal on Computing 40, 5, 1211--1233. Google ScholarDigital Library
- Susanne Albers. 2008. On the value of coordination in network design. In Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’08). 294--303. Google ScholarDigital Library
- Elliot Anshelevich, Anirban Dasgupta, Jon M. Kleinberg, Éva Tardos, Tom Wexler, and Tim Roughgarden. 2004. The price of stability for network design with fair cost allocation. In Proceedings of the 45th Symposium on Foundations of Computer Science (FOCS’04). 295--304. Google ScholarDigital Library
- Baruch Awerbuch, Yossi Azar, and Amir Epstein. 2005. The price of routing unsplittable flow. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC’05). 57--66. Google ScholarDigital Library
- Kshipra Bhawalkar, Martin Gairing, and Tim Roughgarden. 2010. Weighted congestion games: Price of anarchy, universal worst-case examples, and tightness. In Algorithms—ESA 2010. Lecture Notes in Computer Science, Vol. 6347. Springer, 17--28. Google ScholarDigital Library
- Vittorio Bilò. 2012. A unifying tool for bounding the quality of non-cooperative solutions in weighted congestion games. In Proceedings of the 10th International Workshop on Approximation and Online Algorithms (WAOA’12). 215--228.Google Scholar
- Vittorio Bilò and Roberta Bove. 2011. Bounds on the price of stability of undirected network design games with three players. Journal of Interconnection Networks 12, 1--2, 1--17.Google ScholarCross Ref
- Vittorio Bilò, Ioannis Caragiannis, Angelo Fanelli, and Gianpiero Monaco. 2010. Improved lower bounds on the price of stability of undirected network design games. In Proceedings of the 3rd International Symposium on Algorithmic Game Theory (SAGT’10). 90--101. Google ScholarDigital Library
- Vittorio Bilò, Michele Flammini, and Luca Moscardelli. 2013. The price of stability for undirected broadcast network design with fair cost allocation is constant. In Proceedings of the 54th Annual IEEE Symposium on Foundations of Computer Science (FOCS’13). 638--647. Google ScholarDigital Library
- Ioannis Caragiannis, Michele Flammini, Christos Kaklamanis, Panagiotis Kanellopoulos, and Luca Moscardelli. 2011. Tight bounds for selfish and greedy load balancing. Algorithmica 61, 3, 606--637. Google ScholarDigital Library
- Ho-Lin Chen and Tim Roughgarden. 2006. Network design with weighted players. In Proceedings of the 18th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA’06). ACM, New York, NY, 29--38. DOI:http://dx.doi.org/10.1145/1148109.1148114 Google ScholarDigital Library
- George Christodoulou, Christine Chung, Katrina Ligett, Evangelia Pyrga, and Rob van Stee. 2009. On the price of stability for undirected network design. In Proceedings of the 7th Workshop on Approximation and Online Algorithms (WAOA’09). 86--97. Google ScholarDigital Library
- George Christodoulou and Martin Gairing. 2013. Price of stability in polynomial congestion games. In Proceedings of the 40th International Colloquium on Automata, Languages, and Programming (ICALP’13). 496--507. Google ScholarDigital Library
- George Christodoulou and Elias Koutsoupias. 2005a. On the price of anarchy and stability of correlated equilibria of linear congestion games. In Algorithms—ESA 2005. Lecture Notes in Computer Science, Vol. 3669. Springer, 59--70. Google ScholarDigital Library
- George Christodoulou and Elias Koutsoupias. 2005b. The price of anarchy of finite congestion games. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC’05). 67--73. Google ScholarDigital Library
- George Christodoulou, Elias Koutsoupias, and Paul G. Spirakis. 2011. On the performance of approximate equilibria in congestion games. Algorithmica 61, 1, 116--140. Google ScholarDigital Library
- Yann Disser, Andreas Emil Feldmann, Max Klimm, and Matús Mihalák. 2015. Improving the Hk-bound on the price of stability in undirected Shapley network design games. Theoretical Computer Science 562, 557--564. Google ScholarDigital Library
- Amos Fiat, Haim Kaplan, Meital Levy, Svetlana Olonetsky, and Ronen Shabo. 2006. On the price of stability for designing undirected networks with fair cost allocations. In Proceedings of the 33rd International Colloquium on Automata, Languages, and Programming (ICALP’06). 608--618. Google ScholarDigital Library
- Elias Koutsoupias and Christos H. Papadimitriou. 1999. Worst-case equilibria. In Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science (STACS’99). 404--413. Google ScholarDigital Library
- Euiwoong Lee and Katrina Ligett. 2013. Improved bounds on the price of stability in network cost sharing games. In Proceedings of 14th ACM Conference on Electronic Commerce (EC’13). 607--620. Google ScholarDigital Library
- Jian Li. 2009. An O(&frac;log n log log n upper bound on the price of stability for undirected Shapley network design games. Information Processing Letters 109, 15, 876--878. Google ScholarDigital Library
- Dov Monderer and Lloyd S. Shapley. 1996. Potential games. Games and Economics Behavior 14, 124--143.Google ScholarCross Ref
- Robert W. Rosenthal. 1973. A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65--67.Google ScholarDigital Library
- Tim Roughgarden. 2012. Intrinsic robustness of the price of anarchy. Communications of the ACM 55, 7, 116--123. Google ScholarDigital Library
- Andreas S. Schulz and Nicólas E. Stier-Moses. 2002. On the performance of user equilibria in traffic networks. In Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’03). 86--87. Google ScholarDigital Library
Index Terms
- Price of Stability in Polynomial Congestion Games
Recommendations
The price of anarchy of finite congestion games
STOC '05: Proceedings of the thirty-seventh annual ACM symposium on Theory of computingWe consider the price of anarchy of pure Nash equilibria in congestion games with linear latency functions. For asymmetric games, the price of anarchy of maximum social cost is Θ(√N), where N is the number of players. For all other cases of symmetric or ...
Existence and Efficiency of Equilibria for Cost-Sharing in Generalized Weighted Congestion Games
This work studies the impact of cost-sharing methods on the existence and efficiency of (pure) Nash equilibria in weighted congestion games. We also study generalized weighted congestion games, where each player may control multiple commodities. Our ...
On the Performance of Approximate Equilibria in Congestion Games
We study the performance of approximate Nash equilibria for congestion games with polynomial latency functions. We consider how much the price of anarchy worsens and how much the price of stability improves as a function of the approximation factor . ...
Comments