Semi-core equivalence

The main requirements for equivalence of the core of an economy and the Walrasian equilibrium allocations are largeness and the freedom to form almost arbitrary coalitions in the Edgeworthian barter processes. We investigate whether constraints on coalition formation and coalitional barter alter these insights. Our notion of the semi-core imposes a restriction on the collection of formable coalitions that does not affect the fundamental equivalence property. Using our concept of the contract-core we show that additional constraints on coalitional barter can only be alleviated within an environment with sufficiently many formable coalitions: besides a contract-core equivalence theorem we show certain non-equivalence results.