The core and competitive equilibria in finite economies

Abstract

The approach to competitive markets by way of bargaining among traders was developed by Edgeworth (1881). Walras (1874-77) considered markets led by marker managers. In these markers, prices are announced which lead to offers to buy and sell, which are aggregated over the market. Then price lists are revised in the light of supply and demand, upward for an excess demand, downward for an excess supply. Trades are carried out when demand and supply are in balance. On the other hand, Edgeworth considered bargaining between individual traders in which no bargains are final until a point is reached where no group of traders can conclude a new bargain which they prefer to their existing bargains. Edgeworth showed in the simplest case of trading in two goods that such a situation, in which no new bargains are possible which are preferred by some participants, will approach a competitive equilibrium as the number of traders increases indefinitely. This result has been generalized to the case of many goods and to production economies in recent years. The path breaking paper was that of Debreu and Scarf (1963). Most of the results described in this chapter may be found in McKenzie (1988, 1990) and McKenzie and Shinotsuka (1991). There are also similar theorems in Hildenbrand and Kirman (1988). My purpose here is to show precisely where assumptions must be strengthened or may be weakened in establishing the major theorems of the subject for the case of economies with a finite number of agents and a finite number of goods.