The Walrasian objection mechanism and Mas-Colell's bargaining set in economies with many commodities

We study the Walrasian objection mechanism in the framework of economies with a measure space of agents and a separable Banach space of commodities whose positive cone has a non-empty interior. We provide several characterizations of Walrasian objections and use them to study the bargaining set of the economy, as defined in MasColell (J Math Econ 18(2):129-139, 1989). Our main result shows that whenever the measure space of agents is saturated, every non-competitive allocation can be blocked with a Walrasian objection. This implies that the bargaining set, the core and the set of competitive allocations are equivalent solution concepts.