Abstract We study settings where each agent can exert costly effort that creates nonrival, heterogeneous benefits for some of the others. For example, municipalities can forgo consumption to reduce pollution. How do the prospects for efficient cooperation depend on asymmetries in the effects of players' actions? We approach this question by analyzing a network that describes the marginal benefits agents can confer on one another. The first set of results explains how the largest eigenvalue of this network measures the marginal gains available from cooperating; as an application, we describe the players whose participation is essential to achieving any Pareto improvement on an inefficient status quo. Next, we examine mechanisms all of whose equilibria are Pareto efficient and individually rational; an outcome is called robust if it is an equilibrium outcome in every such mechanism. Robust outcomes exist and correspond to the Lindahl public goods solutions. The main result is a characterization of effort levels at these outcomes in terms of players' centralities in the benefits network. It entails that an outcome is robust if and only if agents contribute in proportion to how much they value the efforts of those who help them
