Bottleneck links, variable demand, and the tragedy of the commons

Richard Cole, Yevgeniy Dodis, Tim Roughgarden

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The price of anarchy, a measure of the inefficiency of selfish behavior, has been successfully analyzed in a diverse array of models over the past five years. The overwhelming majority of this work has studied optimization problems that sought an optimal way to allocate a fixed demand to resources whose performance degrades with increasing congestion. While fundamental, such problems overlook a crucial feature of many applications: the intrinsic coupling of the quality or cost of a resource and the demand for that resource. This coupling motivates allowing demand to vary with congestion, which in turn can lead to "the tragedy of the commons" - severe inefficiency caused by the overconsumption of a shared resource. Allowing the demand for resources to vary with their congestion illuminates a second issue with existing studies of the price of anarchy: the standard additive method of aggregating the costs of different resources in a player's strategy is inappropriate for some important applications, including many of those with variable demand. For example, in networking applications a key performance metric is the achievable throughput along a path, which is controlled by its bottleneck (most congested) edge. This disconnect motivates consideration of nonlinear cost aggregation functions, such as the l p norms. In this paper, we initiate the study of the price of anarchy with variable demand and with broad classes of nonlinear aggregation functions. We focus on selfish routing in single- and multicommodity networks, and on the l p norms for 1 ≤ p ≤∞; our main results are as follows. For a natural "prize-collecting" objective function, the price of anarchy in multicommodity networks with variable demand is no larger than that in fixed-demand networks. Thus the inefficiency arising from the tragedy of the commons is no more severe than that from routing inefficiencies. Using the l p norm with 1 < p < ∞ as a cost aggregation function can dramatically increase the price of anarchy in multicommodity networks (relative to additive aggregation), but causes no such additional inefficiency in single-commodity networks. Using the l norm as a cost aggregation function can dramatically increase the price of anarchy, even in single-commodity networks. If attention is restricted to equilibria with additional structure, however - structure that is ensured by distributed shortest-path routing protocols - then using the l norm does not increase the price of anarchy relative to additive aggregation.

Original languageEnglish (US)
Title of host publicationProceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms
Pages668-677
Number of pages10
DOIs
StatePublished - 2006
EventSeventeenth Annual ACM-SIAM Symposium on Discrete Algorithms - Miami, FL, United States
Duration: Jan 22 2006Jan 24 2006

Other

OtherSeventeenth Annual ACM-SIAM Symposium on Discrete Algorithms
CountryUnited States
CityMiami, FL
Period1/22/061/24/06

Fingerprint

Price of Anarchy
Agglomeration
Aggregation Function
Resources
Norm
Congestion
Costs
Cost Function
Aggregation
Selfish Routing
Vary
Routing protocols
Demand
Performance Metrics
Routing Protocol
Throughput
Nonlinear Function
Networking
Shortest path
Routing

ASJC Scopus subject areas

  • Software
  • Discrete Mathematics and Combinatorics
  • Safety, Risk, Reliability and Quality
  • Chemical Health and Safety

Cite this

Cole, R., Dodis, Y., & Roughgarden, T. (2006). Bottleneck links, variable demand, and the tragedy of the commons. In Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms (pp. 668-677) https://doi.org/10.1145/1109557.1109630

Bottleneck links, variable demand, and the tragedy of the commons. / Cole, Richard; Dodis, Yevgeniy; Roughgarden, Tim.

Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms. 2006. p. 668-677.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Cole, R, Dodis, Y & Roughgarden, T 2006, Bottleneck links, variable demand, and the tragedy of the commons. in Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms. pp. 668-677, Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, Miami, FL, United States, 1/22/06. https://doi.org/10.1145/1109557.1109630
Cole R, Dodis Y, Roughgarden T. Bottleneck links, variable demand, and the tragedy of the commons. In Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms. 2006. p. 668-677 https://doi.org/10.1145/1109557.1109630
Cole, Richard ; Dodis, Yevgeniy ; Roughgarden, Tim. / Bottleneck links, variable demand, and the tragedy of the commons. Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms. 2006. pp. 668-677
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