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In this article we show that the price of stability of Shapley network design games on undirected graphs with k players is at most k3(k+1)/2−k21+k3(k+1)/2−k2Hk=(1−Θ(1/k4))Hk, where Hk denotes the k-th harmonic number. This improves on the known upper bound of Hk, which is also valid for directed graphs but for these, in contrast, is tight. Hence, we give the first non-trivial upper bound on the price...
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