Linear Cost Share Equilibria and the Veto Power of the Grand Coalition

We consider pure exchange economies with finitely many private goods involving the choice of a public project. We discuss core-equivalence results in the general framework of non-Euclidean representation of the collective goods. We define a contribution scheme to capture the fraction of the total cost of providing the project that each blocking coalition is expected to cover. We show that for each given contribution scheme defined over the wider class of Aubin coalitions, the resulting core is equivalent to the corresponding linear cost share equilibria. We also characterize linear cost share equilibria in terms of the veto power of the grand coalition. It turns out that linear cost share equilibria are exactly those allocations that cannot be blocked by the grand coalition with reference to auxiliary economies with the same space of agents and modified initial endowments and cost functions. Unlike the Aubin-type equivalence, this characterization does not depend on a particular contribution scheme.