Cost-sharing mechanisms for network design

We consider a single source network design problem from a game-theoretic perspective. Gupta, Kumar and Roughgarden (Proc. 35th Annual ACM STOC, pages 365-372, 2003) developed a simple method for single source rent-or-buy problem that also yields the bestknown approximation ratio for the problem. We show how to use a variant of this method to develop an approximately budget-balanced and group strategyproof cost-sharing method for the problem. The novelty of our approach stems from our obtaining the cost-sharing methods for the rent-or-buy problem by carefully combining cost-shares for the simpler problem Steiner tree problem; we feel that this idea may have wider implications. Our algorithm is conceptually simpler than the previous such cost-sharing method due to Pal and Tardos (Proc. 44th Annual FOCS, pages 584-593, 2003), and has a much improved approximation factor of 4.6 (over the previously known factor of 15).