Fundamental impossibility theorems on voluntary participation in the provision of non-excludable public goods

Groves and Ledyard (Econometrica 45:783–809, 1977) constructed a mechanism attaining Pareto efficient allocations in the presence of public goods. After this path-breaking paper, many mechanisms have been proposed to attain desirable allocations with public goods. Thus, economists have thought that the free-rider problem is solved, in theory. Our view to this problem is not so optimistic. Rather, we propose fundamental impossibility theorems with public goods. In the previous mechanism design, it was implicitly assumed that every agent must participate in the mechanism that the designer provides. This approach neglects one of the basic features of public goods: non-excludability. We explicitly incorporate non-excludability and then show that it is impossible to construct a mechanism in which every agent has an incentive to participate.