We study network games in which players choose partners and an effort level. There is a finite set of players N, each choosing an action si; from an ordered set Si and forming links G, with payoffs ui(G, s). We study two stability concepts: an outcome (G, s) is strictly pairwise stable if (i) actions s are a Nash equilibrium for fixed G; (ii) no player wishes to unilaterally sever an existing link; and (iii) no pair of unlinked players both weakly desire to form a link. The network is strictly pairwise Nash stable if no player can strictly benefit from simultaneously changing their action and severing some links.

This paper introduces a methodology for selecting seeds to maximize contagion using a coarse categorization of individuals. Within a large and flexible class of random graph models, I show how to compute a seed multiplier for each category---the average number of new infections a seed generates---and I propose randomly seeding the category with the highest multiplier. Relative to existing methods for targeted seeding, my approach requires far less computing power---the problem scales with the number of categories, not the number of individuals---and far less data---all we need are estimates for the first two moments of the degree distribution within each category and aggregated relational data on connections between individuals in different categories. I validate the methodology through simulations using real network data.

No abstract available.

We study the perfect Bayesian equilibria of a model of social learning in networks where agents learn about an unknown state of the world by observing the actions of their neighbors. The network topology is drawn from an arbitrary distribution; contrary to prior models in the literature, two agents' sets of neighbors are not assumed to be independent. This extension allows us to capture real-world network phenomena, such as clustering and assortativity, and to consider the performance of social learning in widely used models of social networks, such as preferential attachment models. Since agents only observe the realization of their own neighborhoods, two agents could have vastly different beliefs about the overall network structure, and they may disagree over who is well-informed or well-connected. We call this phenomenon aggregate network uncertainty. This greatly alters our understanding of social learning dynamics and whether networks successfully aggregate dispersed information. Past literature has focused on herding outcomes as the key inefficiency of social learning, but we find that more severe inefficiencies can occur. In addition to the traditional metric of information aggregation, we introduce a second, weaker metric motivated by the notion of an expert, which we define as an outside agent whose private information is at least as strong as that of any other agent in the network. Learning is successful by our metric if all agents perform at least as well as an expert in the limit as society grows. Without aggregate network uncertainty, information aggregation is successful by this metric if and only if a connectivity condition holds. Herding outcomes can only occur once social learning has met our metric of success. With aggregate network uncertainty, there are several ways learning fails to reach even this weaker metric. Our main positive result is a characterization of sufficient conditions for successful information aggregation in the presence of aggregate network uncertainty. We show that information aggregation is successful whenever agents can identify well-connected neighbors with low distortion. Since neighborhoods are correlated, observing an agent may alter the informativeness of that agent's decision; distortion measures the extent to which this phenomenon occurs. We also demonstrate that in special cases our conditions are both necessary and sufficient for successful learning. We use this characterization to show that the popular preferential attachment network model successfully aggregates information.