Adv. Math. Econ. 14, 35-46 (2010)

A Note on Aumann’s Core Equivalence Theorem without Monotonicity ^{1}

Jun Honda^{2} and Shin-Ichi Takekuma^{3}

1 Graduate School of Economics, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo 186-8601, Japan (em071026@g.hit-u.ac.jp)

2 Faculty of Economics, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo 186-8601, Japan (tkkm@econ.hit-u.ac.jp)

Received: June 2, 2009 Revised: October 23, 2009

JEL classification: C71, D41, D51

Mathematical Subject Classification (2000): 28A20, 91A12, 91A13, 91B50

Abstract. In an exchange economy with a continuum of traders, we establish the equivalence theorem on the core and the set of competitive allocations without assuming monotonicity of traders’ preferences. Under weak assumptions 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 assumptions than monotonicity.

Key words: core, equivalence; monotonicity, quasi-equilibrium, irreducibility