2004 | ELLIOT ANSHELEVICH, ANIRBAN DASGUPTA, JON KLEINBERG, ÉVA TARDOS, TOM WEXLER, AND TIM ROUGHGARDEN
The paper analyzes the price of stability in network design games with fair cost allocation. It shows that the price of stability is O(log k), where k is the number of users, under a fair cost-sharing mechanism derived from the Shapley value. This mechanism ensures that the cost of each edge is divided equally among users whose paths include it. The paper proves that the best Nash equilibrium has a cost at most H(k) times the optimal cost, where H(k) is the harmonic number. This result holds even when users are seeking to balance network design costs with latencies, and when the network has only delays and no construction costs. The paper also discusses the convergence time of best-response dynamics and extends the results to weighted games. It shows that the price of stability can be as high as Ω(k) in certain cases. The paper also considers the case of undirected graphs and shows that the bound of H(k) is not tight for undirected graphs. The paper concludes that the fair cost allocation protocol is a useful mechanism for inducing strategic behavior to form near-optimal equilibria.The paper analyzes the price of stability in network design games with fair cost allocation. It shows that the price of stability is O(log k), where k is the number of users, under a fair cost-sharing mechanism derived from the Shapley value. This mechanism ensures that the cost of each edge is divided equally among users whose paths include it. The paper proves that the best Nash equilibrium has a cost at most H(k) times the optimal cost, where H(k) is the harmonic number. This result holds even when users are seeking to balance network design costs with latencies, and when the network has only delays and no construction costs. The paper also discusses the convergence time of best-response dynamics and extends the results to weighted games. It shows that the price of stability can be as high as Ω(k) in certain cases. The paper also considers the case of undirected graphs and shows that the bound of H(k) is not tight for undirected graphs. The paper concludes that the fair cost allocation protocol is a useful mechanism for inducing strategic behavior to form near-optimal equilibria.