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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 ε- Walrasian equilibrium whenever for each ε > 0 there exists some price p not equal to 0 with p ∙ω = 1 (where ω = Σω i is the total endowment) and with x ≥ i x i implying p times x ≥ p ∙ω i – ε. 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 ε-Walrasian equilibrium. Theorem III: If preferences are proper, then every Edgeworth equilibrium is a quasi-equilibrium.
Aliprantis, Charalambos D.; Brown, Donald J.; and Burkinshaw, Owen, "Edgeworth Equilibria" (1985). Cowles Foundation Discussion Papers. 996.