Optimal Provision of a Non-Excludable Public Good

In this paper, we consider the problem that a benevolent designer wants to provide a non-excludable public good with a fixed cost to agents with privately known valuations. Adopting utilitarian's point of view, the designer maximizes the ex-ante total utility of all agents. The impossibility result (e.g., Green and Laffont, 1977) shows that among all strategy-proof mechanisms, none can achieve both allocation efficiency and budget-balanced-ness at the same time. For a canonical model with two agents, we characterize the optimal mechanisms. The optimal mechanisms are always budget-balanced under a large class of well-behaved and commonly used distributions, within all feasible strategy-proof mechanisms, including popular mechanisms like V-C-G mechanisms and budget-balanced mechanisms and beyond. Moreover, the result can be extended to the multi-agent model by imposing one additional "fairness" condition. In particular, under the optimal mechanism agents share the cost equally. We further show that such equal-cost-sharing mechanism can be implemented by a simple voting game where the voting rule is increasing in the cost