We continue the study of the effects of selfish behavior in the network design problem. We provide new bounds for the price of stability for network design with fair cost allocation for undirected graphs. We consider the most general case, for which the best known upper bound is the Harmonic number H n, where n is the number of agents, and the best previously known lower bound is 12/7 ≈ 1.778. We present a nontrivial lower bound of 42/23 ≈ 1.8261. Furthermore, we show that for two players, the price of stability is exactly 4/3, while for three players it is at least 74/48 ≈ 1.542 and at most 1.65. These are the first improvements on the bound of Hn for general networks. In particular, this demonstrates a separation between the price of stability on undirected graphs and that on directed graphs, where Hn is tight. Previously, such a gap was only known for the cases where all players have a shared source, and for weighted players.