A Characterization of Undirected Graphs Admitting Optimal Cost Shares

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10660)


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.


Network cost sharing games Forbidden subgraphs 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut für MathematikUniversität AugsburgAugsburgGermany

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