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

Richard Cole, Yevgeniy Dodis, Tim Roughgarden

Research output: Contribution to journalArticlepeer-review


We study the price of anarchy of selfish routing with variable traffic rates and when the path cost is a nonadditive function of the edge costs. Nonadditive path costs are important, for example, in networking applications, where a key performance metric is the achievable throughput along a path, which is controlled by its bottleneck (most congested) edge. We prove the following results. In multicommodity networks, the worst-case price of anarchy under the ℓ p path cost with 1 < p can be dramatically larger than under the standard ℓ p path cost. In single-commodity networks, the worst-case price of anarchy under the ℓ 1 path cost with 1 < p is no more than with the standard ℓ 1 path norm. (A matching lower bound follows trivially from known results.) This upper bound also applies to the ℓ path cost if and only if attention is restricted to the natural subclass of equilibria generated by distributed shortest path routing protocols. For a natural cost-minimization objective function, the price of anarchy with endogenous traffic rates (and under any ℓ p path cost) is no larger than that in fixed-demand networks. Intuitively, the worst-case inefficiency arising from the "tragedy of the commons" is no more severe than that from routing inefficiencies. ©

Original languageEnglish (US)
Pages (from-to)194-203
Number of pages10
Issue number3
StatePublished - Oct 2012


  • price of anarchy
  • routing
  • shortest path protocols
  • traffic equilibria

ASJC Scopus subject areas

  • Information Systems
  • Computer Networks and Communications


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