skip to main content
research-article

Restoring Pure Equilibria to Weighted Congestion Games

Published: 31 July 2015 Publication History

Abstract

Congestion games model several interesting applications, including routing and network formation games, and also possess attractive theoretical properties, including the existence of and convergence of natural dynamics to a pure Nash equilibrium. Weighted variants of congestion games that rely on sharing costs proportional to players' weights do not generally have pure-strategy Nash equilibria. We propose a new way of assigning costs to players with weights in congestion games that recovers the important properties of the unweighted model. This method is derived from the Shapley value, and it always induces a game with a (weighted) potential function. For the special cases of weighted network cost-sharing and weighted routing games with Shapley value-based cost shares, we prove tight bounds on the worst-case inefficiency of equilibria. For weighted network cost-sharing games, we precisely calculate the price of stability for any given player weight vector, while for weighted routing games, we precisely calculate the price of anarchy, as a parameter of the set of allowable cost functions.

References

[1]
S. Aland, D. Dumrauf, M. Gairing, B. Monien, and F. Schoppmann. 2011. Exact price of anarchy for polynomial congestion games. SIAM J. Comput. 40, 5, 1211--1233.
[2]
E. Anshelevich, A. Dasgupta, J. Kleinberg, É. Tardos, T. Wexler. and T. Roughgarden. 2008. The price of stability for network design with fair cost allocation. SIAM J. Comput. 38, 4, 1602--1623.
[3]
B. Awerbuch, Y. Azar, and L. Epstein. 2005. The price of routing unsplittable flow. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC). 57--66.
[4]
K. Bhawalkar, M. Gairing, and T. Roughgarden. 2010. Weighted congestion games: Price of anarchy, universal worst-case examples, and tightness. In Proceedings of the 18th Annual European Symposium on Algorithms (ESA). Vol. 2. 17--28.
[5]
H. Chen and T. Roughgarden. 2009. Network design with weighted players. Theor. Comput. Syst. 45, 2, 302-324.
[6]
H. Chen, T. Roughgarden, and G. Valiant. 2010. Designing network protocols for good equilibria. SIAM J. Comput. 39, 5, 1799--1832.
[7]
D. Fotakis, S. C. Kontogiannis, and P. G. Spirakis. 2005. Selfish unsplittable flows. Theor. Comput. Sci. 348, 2-3, 226--239.
[8]
M. Gairing and F. Schoppmann. 2007. Total latency in singleton congestion games. In Proceedings of the 7th International Workshop on Internet and Network Economies (WINE). 381--387.
[9]
M. X. Goemans, V. Mirrokni, and A. Vetta. 2005. Sink equilibria and convergence. In Proceedings of the 46th Annual Symposium on Foundations of Computer Science (FOCS). 142--151.
[10]
R. Gopalakrishnan, J. R. Marden, and A. Wierman. 2013. Potential games are necessary to ensure pure Nash equilibria in cost sharing games. In Proceedings of the 14th ACM Conference on Electronic Commerce (EC). 563--564.
[11]
T. Harks and M. Klimm. 2012. On the existence of pure nash equilibria in weighted congestion games. Math. Oper. Res. 37, 3, 419--436.
[12]
T. Harks, M. Klimm, and R. H. Möhring. 2011. Characterizing the existence of potential functions in weighted congestion games. Theor. Comput. Syst. 49, 1, 46--70.
[13]
S. Hart and A. Mas-Colell. 1989. Potential, value, and consistency. Econometrica 57, 3, 589-614.
[14]
E. Kalai and D. Samet. 1987. On weighted shapley values. Int. J. Game Theor. 16, 3, 205-222.
[15]
E. Koutsoupias and C. H. Papadimitriou. 1999. Worst-case equilibria. In Proceedings of the 16th Annual Symposium on Theoretical Aspects of Computer Science (STACS). 404--413.
[16]
J. R. Marden and A. Wierman. 2013. Distributed welfare games. Oper. Res. 61, 1, 155--168.
[17]
I. Milchtaich. 1996. Congestion games with player-specific payoff functions. Games Econ. Behav. 13, 1, 111--124.
[18]
D. Monderer and L. S. Shapley. 1996. Potential games. Games Econ. Behav. 14, 1, 124--143.
[19]
D. Mosk-Aoyama and T. Roughgarden. 2009. Worst-case efficiency analysis of queueing disciplines. In Proceedings of the 36th International Colloqium on Automata, Languages and Programming (ICALP). 546--557.
[20]
H. Moulin. 2008. The price of anarchy of serial, average and incremental cost sharing. Econo. Theor. 36, 3, 379--405.
[21]
M. J. Osborne and A. Rubinstein. 1994. A Course in Game Theory. MIT Press.
[22]
R. W. Rosenthal. 1973a. A class of games possessing pure-strategy nash equilibria. Int. J. Game Theor. 2, 1, 65--67.
[23]
R. W. Rosenthal. 1973b. The network equilibrium problem in integers. Networks 3, 1, 53--59.
[24]
T. Roughgarden. 2009. Intrinsic robustness of the price of anarchy. In Proceedings of the 41st ACM Symposium on Theory of Computing (STOC). 513.
[25]
T. Roughgarden. 2012. The price of anarchy in games of incomplete information. In Proceedings of the 13th ACM Conference on Electronic Commerce (EC). 862--879.
[26]
T. Roughgarden and É. Tardos. 2002. How bad is selfish routing? J. ACM 49, 2, 236--259.
[27]
L. S. Shapley. 1953. Additive and Non-Additive Set Functions. Ph.D. Dissertation. Department of Mathematics, Princeton University.
[28]
S. J. Shenker. 1995. Making greed work in networks: a game-theoretic analysis of switch service disciplines. IEEE/ACM Tran. Netw. 3, 6, 819--831.
[29]
V. Syrgkanis. 2012. Bayesian games and the smoothness framework. arXiv.cs.GT:1203.5155v1.

Cited By

View all
  • (2024)Price of Anarchy in mmWave Backhaul Routing and Link SchedulingIEEE Transactions on Cognitive Communications and Networking10.1109/TCCN.2024.336691010:4(1496-1510)Online publication date: Aug-2024
  • (2023)Equilibrium Analysis of Customer Attraction GamesWeb and Internet Economics10.1007/978-3-031-48974-7_14(242-255)Online publication date: 4-Dec-2023
  • (2022)Improved Price of Anarchy via PredictionsProceedings of the 23rd ACM Conference on Economics and Computation10.1145/3490486.3538296(529-557)Online publication date: 12-Jul-2022
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Economics and Computation
ACM Transactions on Economics and Computation  Volume 3, Issue 4
Special Issue on WINE '13 and Regular Papers
July 2015
186 pages
ISSN:2167-8375
EISSN:2167-8383
DOI:10.1145/2810066
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 31 July 2015
Accepted: 01 December 2014
Revised: 01 November 2014
Received: 01 July 2014
Published in TEAC Volume 3, Issue 4

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. Weighted congestion games
  2. price of anarchy
  3. price of stability
  4. weighted Shapley value

Qualifiers

  • Research-article
  • Research
  • Refereed

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)22
  • Downloads (Last 6 weeks)1
Reflects downloads up to 17 Jan 2025

Other Metrics

Citations

Cited By

View all
  • (2024)Price of Anarchy in mmWave Backhaul Routing and Link SchedulingIEEE Transactions on Cognitive Communications and Networking10.1109/TCCN.2024.336691010:4(1496-1510)Online publication date: Aug-2024
  • (2023)Equilibrium Analysis of Customer Attraction GamesWeb and Internet Economics10.1007/978-3-031-48974-7_14(242-255)Online publication date: 4-Dec-2023
  • (2022)Improved Price of Anarchy via PredictionsProceedings of the 23rd ACM Conference on Economics and Computation10.1145/3490486.3538296(529-557)Online publication date: 12-Jul-2022
  • (2021)Equilibrium Inefficiency and Computation in Cost-Sharing Games in Real-Time Scheduling SystemsAlgorithms10.3390/a1404010314:4(103)Online publication date: 25-Mar-2021
  • (2020)Existence and Efficiency of Equilibria for Cost-Sharing in Generalized Weighted Congestion GamesACM Transactions on Economics and Computation10.1145/33914348:2(1-28)Online publication date: 13-May-2020
  • (2020)Approximating Generalized Network Design under (Dis)economies of Scale with Applications to Energy EfficiencyJournal of the ACM10.1145/337738767:1(1-33)Online publication date: 7-Feb-2020
  • (2020)A Fairness-aware Incentive Scheme for Federated LearningProceedings of the AAAI/ACM Conference on AI, Ethics, and Society10.1145/3375627.3375840(393-399)Online publication date: 7-Feb-2020
  • (2020)A Sustainable Incentive Scheme for Federated LearningIEEE Intelligent Systems10.1109/MIS.2020.298777435:4(58-69)Online publication date: 1-Jul-2020
  • (2020)Equilibrium Inefficiency in Resource Buying Games with Load-Dependent CostsAlgorithmic Game Theory10.1007/978-3-030-57980-7_6(83-98)Online publication date: 16-Sep-2020
  • (2019)Federated LearningSynthesis Lectures on Artificial Intelligence and Machine Learning10.2200/S00960ED2V01Y201910AIM04313:3(1-207)Online publication date: 19-Dec-2019
  • Show More Cited By

View Options

Login options

Full Access

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media