Endogenous formation of networks for local public goods

Abstract

The paper studies a situation in which agents can make a binding agreement both on the amount of local public goods and on the structure of networks through which they share the benefits of public goods. An agent enjoys the benefit of public goods produced by other agents who are (directly or indirectly) connected to him. There is a cost to maintain a link as well as to produce a public good. Because agents can choose the amount of public goods, the value of a link is endogenously determined. We consider two different models of sequential bargaining games through which a contract on allocations is established. In the first model, we allow agents to propose a pure allocation and show that there is no symmetric stationary perfect equilibrium for sufficiently patient agents. In the second model, agents are allowed to propose a distribution on allocations. As a result, we find a symmetric stationary perfect equilibrium in which probabilistic choices are made on an equivalent class of allocations. Subsequently, we characterize core allocations, which consist of a minimally connected network and an effort profile, in which at most one agent does not produce the maximum amount of public good.