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A Characterization of Undirected Graphs Admitting Optimal Cost Shares

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Web and Internet Economics (WINE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10660))

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Abstract

In a seminal paper, Chen et al. [7] studied cost sharing protocols for network design with the objective to implement a low-cost Steiner forest as a Nash equilibrium of an induced cost-sharing game. One of the most intriguing open problems to date is to understand the power of budget-balanced and separable cost sharing protocols in order to induce low-cost Steiner forests.

In this work, we focus on undirected networks and analyze topological properties of the underlying graph so that an optimal Steiner forest can be implemented as a Nash equilibrium (by some separable cost sharing protocol) independent of the edge costs. We term a graph efficient if the above stated property holds. As our main result, we give a complete characterization of efficient undirected graphs for two-player network design games: an undirected graph is efficient if and only if it does not contain (at least) one out of few forbidden subgraphs. Our characterization implies that several graph classes are efficient: generalized series-parallel graphs, fan and wheel graphs and graphs with small cycles.

This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - HA 8041/1-1.

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Notes

  1. 1.

    Uniform protocols require that the cost shares on an edge only depend on the edge cost and the set of players, but not on the network itself.

  2. 2.

    The certificate for optimality uses a characterization of uniform protocols by Gopalakrishnan et al. [19].

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Authors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, 86135, Augsburg, Germany

    Tobias Harks, Anja Huber & Manuel Surek

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  1. Tobias Harks
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  2. Anja Huber
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  3. Manuel Surek
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Correspondence to Manuel Surek .

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Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Nikhil R. Devanur

  2. Shanghai University of Finance and Economics, Shanghai, China

    Pinyan Lu

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Harks, T., Huber, A., Surek, M. (2017). A Characterization of Undirected Graphs Admitting Optimal Cost Shares. In: R. Devanur, N., Lu, P. (eds) Web and Internet Economics. WINE 2017. Lecture Notes in Computer Science(), vol 10660. Springer, Cham. https://doi.org/10.1007/978-3-319-71924-5_17

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  • DOI: https://doi.org/10.1007/978-3-319-71924-5_17

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