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.
Keywords Impossibility theorems - Voluntary participation - Non-excludable public goods - Lindahl equilibrium - Voluntary contribution mechanism - Olson’s conjecture
JEL Classification C72 - D71 - D78 - H41
We thank an anonymous referee and Takeshi Suzuki for useful comments. Research was partially supported by the Grant in Aid
for Scientific Research of the Ministry of Education, Culture, Sports, Science and Technology in Japan. Yamato thanks the
Division of the Humanities and Social Sciences at the California Institute of Technology for their hospitality during the
period when this draft was written.