Existence and Optimality of Cost Share Equilibria

We consider pure exchange economies with finitely many private goods including also non- Samuelsonian public goods. For this type of economies, the notion of competitive equilibrium called cost share equilibrium is founded on individual payments for public goods varying according to individual benefits. This situation naturally arises when a level of provision is interpreted as a whole configuration of public policies or when cost share functions are interpreted as voluntary contributions instead of predetermined tax systems (Mas Colell (1980)). We establish the equivalence of cost share equilibria with cooperative and non-cooperative game-theoretic solutions. In particular: 1. we characterize cost share equilibria as those allocations which cannot be improved upon by the society; 2. we characterize cost share equilibria as Nash equilibria of a game with two players. Then we discuss the existence of cost share equilibria in economies with public projects satisfying standard assumptions and provide a condition for the set of cost share equilibria to be non-empty. Our analysis of cooperative solutions is based on contribution schemes which capture the fraction of the total cost of collective goods that each coalition of agents is expected to cover.