Natural implementation in public goods economies

In this paper, we identify necessary and sufficient conditions for social choice correspondences to be Nash implemented by “natural” mechanisms in economies with arbitrary numbers of private and public goods. We find that when there exist only one public good and an arbitrary number of private goods, the Lindahl correspondence is implementable by a natural quantity mechanism in which each agent announces his own consumption bundle of private goods and input vectors for public goods. However, regardless of the numbers of private and public goods, the Pareto correspondence is not implementable even by any natural price ⁿ -quantity mechanism in which each agent reports a price vector of private goods and all agents’ personalized price vectors of public goods, in addition to his own consumption bundle of private goods and input vectors for public goods.