Characterizations of equilibrium allocations in an economy with public goods and infinitely many commodities

This paper examines the characterizations of equilibrium in economies with public projects. Public goods, as discussed by Mas-Colell (1980), are modeled as elements of an abstract set lacking a unified ordering structure. We introduce the concepts of cost share equilibrium for such economies, where the private commodity space is a (possibly nonseparable) Banach lattice. Within this framework, we present two distinct characterizations of cost share equilibria via the veto power of the grand coalition in economies featuring finitely many agents. The first characterization involves allocations that are Aubin non-dominated, while the second establishes that an allocation is a cost share equilibrium if and only if it cannot be dominated by the grand coalition, where domination is considered under specific perturbations of initial endowments.