Edgeworth Equilibria

The paper studies pure exchange economies with infinite dimensional commodity spaces in the setting of Riesz dual systems. Several new concepts of equilibrium are introduced. An allocation (x_{1},...,x_{m}) is said to be a) an Edgeworth equilibrium whenever it belongs to the core of every n-fold replication of the economy; and b) an epsilon > 0 there exists some price p not equal to 0 with p omega =1 (where omega = Sigma omega_{i} is the total endowment) and with x >=_{i} x_{i} implying p times x > p times omega_{i} - epsilon. The major results of the paper are the following: Theorem I: Edgeworth equilibria exist. Theorem II: An allocation is an Edgeworth equilibrium if and only if it is an epsilon-Walrasian equilibrium. Theorem III: If preferences are proper, then every Edgeworth equilibrium is a quasi-equilibrium.