The pure theory of public goods: Efficiency, decentralization, and the core

We extend the findings of Mas-Colell on valuation equilibria and the relationship of cost-share equilibria with the core. We allow for any finite number of private goods and a set of public projects without any structure. We show the two welfare theorems for valuation equilibrium, the inclusion of the set of cost-share equilibria in the core, and the nonequivalence of these two sets for an economy with a finite number of agents.