In this paper, we consider the Shapley network design game on undirected networks. In this game, we have an edge weighted undirected network G(V, E) and n selfish players where player i wants to choose a path from source vertex s i to destination vertex t i . The cost of each edge is equally split among players who pass it. The price of stability is defined as the ratio of the cost of the best Nash equilibrium to that of the optimal solution. We present an O(log n/ log log n) upper bound on price of stability for the single sink case, i.e, t i = t for all i.
In the case of undirected networks, an upper bound of O( log n log log n ) on the PoS in single-source games was established by REF .
An $O({\log n\over \log\log n})$ Upper Bound on the Price of Stability for Undirected Shapley Network Design Games
Information Processing Letters archive Volume 109 Issue 15, July, 2009 Pages 876-878
Mathematics Computer Science