Network Cost-Sharing without Anonymity

  • Tim Roughgarden
  • Okke Schrijvers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8768)


We consider network cost-sharing games with non-anonymous cost functions, where the cost of each edge is a submodular function of its users, and this cost is shared using the Shapley value. The goal of this paper is to identify well-motivated equilibrium refinements that admit good worst-case approximation bounds. Our primary results are tight bounds on the cost of strong Nash equilibria and potential function minimizers in network cost-sharing games with non-anonymous cost functions, parameterized by the set \(\mathcal{C}\) of allowable submodular cost functions. These two worst-case bounds coincide for every set \(\mathcal{C}\), and equal the summability parameter introduced in [31] to characterize efficiency loss in a family of cost-sharing mechanisms. Thus, a single parameter simultaneously governs the worst-case inefficiency of network cost-sharing games (in two incomparable senses) and cost-sharing mechanisms. This parameter is always at most the kth Harmonic number \(\mathcal{H}_k \approx \ln k\), where k is the number of players, and is constant for many function classes of interest.


Cost Function Nash Equilibrium Cost Share Congestion Game Submodular Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Tim Roughgarden
    • 1
  • Okke Schrijvers
    • 1
  1. 1.Stanford UniversityStanfordUSA

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