We study the formation of networks in environments where agents derive benefits from their neighbours (immediate links) but suffer losses through contagion when any agent on a path that connects them is hit by a shock. We first consider networks with undirected links (e.g. epidemics, underground resistance organizations, trade networks). We find that the only networks that satisfy strong notions of stability are comprised of disjoint subgraphs that are complete. Then, we consider networks with directed links and we find that stable networks can be asymmetric, connected but not completely connected, thus capturing the main features of production and financial networks. We also identify a trade-off between efficiency and stability.

Suppose that in symmetric aggregative games, in which payoffs depend only on a player's strategy and on an aggregate of all players' strategies, players have conjectures about the reaction of the aggregate to marginal changes in their strategy. The players play a conjectural variation equilibrium, which determines their fitness payoffs. The paper shows that only consistent conjectures can be evolutionarily stable in an infinite population, where a conjecture is consistent if it is equal to the marginal change in the aggregate determined by the actual best responses. In the finite population case, only zero conjectures representing aggregate-taking behavior can be evolutionarily stable.