Mathematical Programming

, Volume 131, Issue 1, pp 333–364

Design of price mechanisms for network resource allocation via price of anarchy


    • Department of Industrial Engineering and Operations ResearchUniversity of California
  • Jiawei Zhang
    • Stern School of BusinessNew York University
Open AccessFull Length Paper Series A

DOI: 10.1007/s10107-010-0379-1


We study the design of price mechanisms for communication network problems in which a user’s utility depends on the amount of flow she sends through the network, and the congestion on each link depends on the total traffic flows over it. The price mechanisms are characterized by a set of axioms that have been adopted in the cost-sharing games, and we search for the price mechanisms that provide the minimum price of anarchy. We show that, given the non-decreasing and concave utilities of users and the convex quadratic congestion costs in each link, if the price mechanism cannot depend on utility functions, the best achievable price of anarchy is \({{4(3-2 \sqrt{2}) \approx 31.4 \% }}\). Thus, the popular marginal cost pricing with price of anarchy less than 1/3 ≈ 33.3% is nearly optimal. We also investigate the scenario in which the price mechanisms can be made contingent on the users’ preference profile while such information is available.

Mathematics Subject Classification (2000)



We thank the anonymous reviewers for very insightful and constructive comments that significantly improved the quality of this paper. We also benefited from the discussions with Herve Moulin and seminar participants at NYU. Ying-Ju Chen gratefully acknowledges the financial support from Chiang Ching-Kuo Foundation (JS002-A-08), and Faculty Research Grant from Committee on Research at UC Berkeley. Jiawei Zhang would like to acknowledge the support by NSF grant 0654116. All remaining errors are our own.

Open Access

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© The Author(s) 2010