2014/06/13 by Akaki Mamageishvili, Mamageishvili, Akaki, Matúš Mihaľák +4
Computer Science · Decision Sciences · Economics, Econometrics and Finance · #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #Game Theory and Applications #Game Theory and Voting Systems #cs.GT
paper · pdf · doi:10.48550/arxiv.1406.3597
arxiv created 2014/06/13 · openalex publication_date 2014/06/13 · arxiv updated 2014/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the network design game with n players, every player chooses a path in an edge-weighted graph to connect her pair of terminals, sharing costs of the edges on her path with all other players fairly. We study the price of stability of the game, i.e., the ratio of the social costs of a best Nash equilibrium (with respect to the social cost) and of an optimal play. It has been shown that the price of stability of any network design game is at most Hn, the n-th harmonic number. This bound is tight for directed graphs. For undirected graphs, the situation is dramatically different, and tight bounds are not known. It has only recently been shown that the price of stability is at most Hn (1-(1)/(Θ(n4)) ), while the worst-case known example has price of stability around 2.25. In this paper we improve the upper bound considerably by showing that the price of stability is at most Hn/2 + ε for any ε starting from some suitable n ≥ n(ε).