Polynomial time equilibria in bottleneck congestion games

Costas Busch, Rajgopal Kannan

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

Abstract

We consider bottleneck congestion games in an arbitrary graph G where player strategies are flows in G. The player's objective is to select a flow that minimizes the maximum load on any edge, that is, minimize the bottleneck congestion. We consider splittable and unsplittable games with pure strategies. It has been an open problem for many years to determine whether it is possible to compute in polynomial time Nash equilibriums for bottleneck congestion games in arbitrary graphs. For splittable games we provide a polynomial time algorithm to compute a Nash equilibrium which is also a global optimum. The unsplittable game problem is known to be PLS-complete, and so we focus on approximate Nash equilibria where players are approximately stable. For uniform player demands we give an algorithm to compute a O(logm)-approximate unsplittable equilibrium in polynomial time, where m is the number of edges. For non-uniform player demands we give an algorithm to compute a O(log(m))-approximate unsplittable equilibrium in polynomial time, where = O(1 + log(dmax/dmin)) and dmax, dmin are the respective maximum and minimum player demands. To our knowledge, these are the first general results for efficiently computing equilibria of pure bottleneck congestion games in arbitrary graphs, both for the splittable and unsplittable cases.

Original languageEnglish (US)
Title of host publicationACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery, Inc
Pages393-409
Number of pages17
ISBN (Electronic)9781450358293
DOIs
StatePublished - Jun 11 2018
Externally publishedYes
Event19th ACM Conference on Economics and Computation, EC 2018 - Ithaca, United States
Duration: Jun 18 2018Jun 22 2018

Publication series

NameACM EC 2018 - Proceedings of the 2018 ACM Conference on Economics and Computation

Conference

Conference19th ACM Conference on Economics and Computation, EC 2018
CountryUnited States
CityIthaca
Period6/18/186/22/18

Keywords

  • Arbitrary graphs
  • Bottleneck congestion
  • Equilibrium computation
  • Nash equilibrium
  • Polynomial time

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Statistics and Probability
  • Computational Mathematics
  • Economics and Econometrics

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