Natural implementation in public goods economies

In this paper, we examine what kinds of social choice correspondences (SCCs) are implementable in Nash equilibria by “natural” mechanisms in divisible pure public goods economies. Then, we found conditions for SCCs to be Nash implementable by each of these four natural mechanisms. These characterizations of SCCs depend on the number of goods. First, regardless of the number of goods, the class of Pareto efficient SCCs implemented by PQ mechanisms is equivalent to that of Pareto efficient SCCs implemented by PQ mechanisms. Second, in the case where there exists only one public good, Q, IPQ, PQ and PQ mechanisms implement the Lindahl correspondence for any number of private goods. But, the Pareto correspondence is not implemented by Q, IPQ, PQ or PQ mechanisms, regardless of the number of goods. Journal of Economic Literature Classification Numbers: C72, D78, H41.