research-article

Existence and Efficiency of Equilibria for Cost-Sharing in Generalized Weighted Congestion Games

Authors:

Martin Gairing,

Kostas Kollias,

Grammateia KotsialouAuthors Info & Claims

ACM Transactions on Economics and Computation (TEAC), Volume 8, Issue 2

Article No.: 11, Pages 1 - 28

https://doi.org/10.1145/3391434

Published: 13 May 2020 Publication History

Abstract

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 results are fairly general; we only require that our cost-sharing method and our set of cost functions satisfy certain natural conditions. For general weighted congestion games, we study the existence of pure Nash equilibria in the induced games, and we exhibit a separation from the standard single-commodity per player model by proving that the Shapley value is the only cost-sharing method that guarantees existence of pure Nash equilibria. With respect to efficiency, we present general tight bounds on the price of anarchy, which are robust and apply to general equilibrium concepts. Our analysis provides a tight bound on the price of anarchy, which depends only on the used cost-sharing method and the set of allowable cost functions. Interestingly, the same bound applies to weighted congestion games and generalized weighted congestion games. 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 provide a somewhat 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. Again, our bounds on the price of stability are independent on whether players are single or multi-commodity.

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Cited By

Chen SBayiz YFridovich-Keil DTopcu U(2025)Relationship design for socially-aware behavior in static gamesAutonomous Agents and Multi-Agent Systems10.1007/s10458-025-09699-439:1Online publication date: 5-Mar-2025
https://doi.org/10.1007/s10458-025-09699-4
Caragiannis IJiang ZSaha BServedio R(2023)Computing Better Approximate Pure Nash Equilibria in Cut Games via Semidefinite ProgrammingProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585236(710-722)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585236
Deng XLi NLi WQi Q(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
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Index Terms

Existence and Efficiency of Equilibria for Cost-Sharing in Generalized Weighted Congestion Games
1. Theory of computation
  1. Theory and algorithms for application domains
    1. Algorithmic game theory and mechanism design

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Published In

cover image ACM Transactions on Economics and Computation

ACM Transactions on Economics and Computation Volume 8, Issue 2

May 2020

173 pages

ISSN:2167-8375

EISSN:2167-8383

DOI:10.1145/3397966

Editors:
David Pennock
Microsoft
,
Ilya Segal
Stanford University

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Copyright © 2020 ACM.

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]

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Association for Computing Machinery

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Publication History

Published: 13 May 2020

Online AM: 07 May 2020

Accepted: 01 February 2020

Revised: 01 June 2019

Received: 01 September 2018

Published in TEAC Volume 8, Issue 2

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Cited By

Chen SBayiz YFridovich-Keil DTopcu U(2025)Relationship design for socially-aware behavior in static gamesAutonomous Agents and Multi-Agent Systems10.1007/s10458-025-09699-439:1Online publication date: 5-Mar-2025
https://doi.org/10.1007/s10458-025-09699-4
Caragiannis IJiang ZSaha BServedio R(2023)Computing Better Approximate Pure Nash Equilibria in Cut Games via Semidefinite ProgrammingProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585236(710-722)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585236
Deng XLi NLi WQi Q(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
https://dl.acm.org/doi/10.1007/978-3-031-48974-7_14
Zhang LKhalgui MLi ZZhang Y(2022)Fairness concern‐based coordinated vehicle route guidance using an asymmetrical congestion gameIET Intelligent Transport Systems10.1049/itr2.1220516:9(1236-1248)Online publication date: Jun-2022
https://doi.org/10.1049/itr2.12205
Fielbaum AKucharski RCats OAlonso-Mora J(2022)How to split the costs and charge the travellers sharing a ride? aligning system’s optimum with users’ equilibriumEuropean Journal of Operational Research10.1016/j.ejor.2021.11.041301:3(956-973)Online publication date: Sep-2022
https://doi.org/10.1016/j.ejor.2021.11.041

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