Summary: On the Value of Coordination in Network Design
We study network design games where n self-interested agents have to form a network by purchasing
links from a given set of edges. We consider Shapley cost sharing mechanisms that split the cost of an
edge in a fair manner among the agents using the edge. It is well known that the price of anarchy of these
games is as high as n. Therefore, recent research has focused on evaluating the price of stability, i.e. the
cost of the best Nash equilibrium relative to the social optimum.
In this paper we investigate to which extent coordination among agents can improve the quality of
solutions. We resort to the concept of strong Nash equilibria, which were introduced by Aumann and are
resilient to deviations by coalitions of agents. We analyze the price of anarchy of strong Nash equilibria
and develop lower and upper bounds for unweighted and weighted games in both directed and undirected
graphs. These bounds are tight or nearly tight for many scenarios. It shows that using coordination, the
price of anarchy drops from linear to logarithmic bounds.
We complement these results by also proving the first super-constant lower bound on the price of sta-
bility of standard equilibria (without coordination) in undirected graphs. More specifically, we show a
lower bound of (log W/ log log W) for weighted games, where W is the total weight of all the agents.
This almost matches the known upper bound of O(log W). Our results imply that, for most settings, the
worst-case performance ratios of strong coordinated equilibria are essentially always as good as the per-
formance ratios of the best equilibria achievable without coordination. These settings include unweighted