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International Symposium on Algorithmic Game Theory

SAGT 2014: Algorithmic Game Theory pp 134–145Cite as

Network Cost-Sharing without Anonymity

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 8768))

Abstract

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.

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Authors and Affiliations

  1. Stanford University, Stanford, CA, 94305, USA

    Tim Roughgarden & Okke Schrijvers

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  1. Tim Roughgarden
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  2. Okke Schrijvers
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Editors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion Israel Institute of Technology, Israel

    Ron Lavi

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Roughgarden, T., Schrijvers, O. (2014). Network Cost-Sharing without Anonymity. In: Lavi, R. (eds) Algorithmic Game Theory. SAGT 2014. Lecture Notes in Computer Science, vol 8768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44803-8_12

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  • DOI: https://doi.org/10.1007/978-3-662-44803-8_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44802-1

  • Online ISBN: 978-3-662-44803-8

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