Suppose that agents can exert costly effort that creates nonrival, heterogeneous benefits for each other. At each possible outcome, a weighted, directed network describing marginal externalities is defined. We show that Pareto efficient outcomes are those at which the largest eigenvalue of the network is 1. An important set of efficient solutions—Lindahl outcomes—are characterized by contributions being proportional to agents’ eigenvector centralities in the network. The outcomes we focus on are motivated by negotiations. We apply the results to identify who is essential for Pareto improvements, how to efficiently subdivide negotiations, and whom to optimally add to a team.

We model the strategic provision of advice in environments where a principal's optimal action depends on an unobserved, binary state of interest. Experts receive signals about the state and each recommends an action. The principal and all experts dislike making errors in their decision and recommendations, respectively, but may have different costs of different errors. Is it in the principal's interest to let experts share information? Although sharing improves experts' ability to avoid errors, we identify a simple environment in which any principal, regardless of how he trades off the different errors, is worse off if he permits information sharing.

We study cascades of failures in a network of interdependent financial organizations: how discontinuous changes in asset values (e.g., defaults and shutdowns) trigger further failures, and how this depends on network structure. Integration (greater dependence on counterparties) and diversification (more counterparties per organization) have different, nonmonotonic effects on the extent of cascades. Diversification connects the network initially, permitting cascades to travel; but as it increases further, organizations are better insured against one another's failures. Integration also faces trade-offs: increased dependence on other organizations versus less sensitivity to own investments. Finally, we illustrate the model with data on European debt cross-holdings.