Properties of the Core in Finite Economies

Abstract

The Edgeworthian concept of the core is based on recontracting by all formable trade coalitions in the economy. In a finite exchange system with sovereign agents $\mathbb{E}{_f}$ this is assumed to be the collection of all coalitions 2^A ≡ { E|E ⊂ A}. Hence, any E ⊂ A is potentially able to improve upon a proposed allocation f ∈ L(f, ℝ ^ℓ₊ ). The main aspect of the Edgeworthian recontracting process is that it describes a system of coordinated economic trade activities. Hildenbrand (1974), Anderson (1986 and 1992), and Hildenbrand and Kirman (1988) are among those who recognize these Edgeworthian trade processes to be the most plausible description of economic interaction in the setting of a finite exchange system. Thus, the core C $\mathbb{E}{_f}$ is recognized as the proper equilibrium concept for the description of economic behavior in a finite exchange system $\mathbb{E}{_f}$. On the other hand we recognize the collection of Walrasian equilibrium allocations W$\mathbb{E}{_f}$ resulting from an ideal, perfectly competitive market system as a benchmark regarding the core, in particular since Walrasian equilibrium allocations have very appealing efficiency and equity properties. This forms the basis for an investigation of the relation between the core as a description of actual results of trade processes in $\mathbb{E}{_f}$ and the Walrasian equilibrium allocations as desirable outcomes of these trade processes. This investigation is the subject of this chapter.