Strategic analysis in complex networks with local externalities

In this paper, we discuss a model with local positive externalities on a complex random network that allows for wide heterogeneities among the agents. The situation can be analyzed as a game of incomplete information where each player's connectivity is her type. We focus on three paradigmatic cases in which the overall degree distribution is Poisson, exponential, and scale-free (given by a power law). For each of them, we characterize the equilibria and obtain interesting insights on the interplay between network topology and payoffs. For example, we reach the somewhat paradoxical conclusion that a broad degree distribution or/and too low a cost of effort render it difficult, if not impossible, to sustain an (efficient) high-effort configuration at equilibrium.