A Note on Aumann’s Core Equivalence Theorem without Monotonicity

In an exchange economy with a continuum of traders, we establish the equivalence theorem on the core and the set of competitive allocations with-out assuming monotonicity of traders ’ preferences. Under weak assump-tions we provide two alternative core equivalence theorems. The first one is for irreducible economies under Debreu’s assumption on quasi-equilibria. The second one is an extension of Aumann’s theorem under weaker assump-tions than monotonicity