Concave Measures and the Fuzzy Core of Exchange Economies with Heterogeneous Divisible Commodities

The main purpose of this paper is to prove the existence of the fuzzy core of an exchange economy with a heterogeneous divisible commodity in which preferences of players are concave measures defined on a σ-algebra of admissible pieces of the total endowment of the commodity. The problem is formulated as the partitioning of a measurable space among finitely many players. Applying the Yosida– Hewitt decomposition theorem, we also demonstrate that partitions in the fuzzy core are supported by prices in L1.