Edgeworth and Walras equilibria of an arbitrage-free exchange economy

In this paper, we first give a direct proof of the existence of Edgeworth equilibria for exchange economies with (possibly) unbounded below consumption sets. The key assumption is that the individually rational utility set is compact. It is worth noticing that the statement of this result and its proof do not depend on the dimension or the particular structure of the commodity space. In a second part of the paper, we give conditions in order to decentralize Edgeworth allocations by continuous prices in a finite dimensional and in an infinite dimensional setting. keywords and phrases: arbitrage-free asset markets, individually rational utility set, Edgeworth equilibria, fuzzy coalitions, fuzzy core, Walras equilibria, quasiequilibria, M -properness.