Bargaining set and anonymous core without the monotonicity assumption

We give an example of an atomless exchange economy in which consumers' preference relations are not monotone and in which the bargaining set of Mas-Colell [ Mas-Colell, A., 1989. An equivalence theorem for a bargaining set. Journal of Mathematical Economics 18, 129-139] consists of all allocations satisfying resource constraints, although the set of all Walrasian equilibrium allocations, the core, and the anonymous core of Hara [Hara, C., 2002. The anonymous core of an exchange economy. Journal of Mathematical Economics 38, 91-116] are all empty. We also give an equivalence theorem for the anonymous core when the preference relations may not be monotone.