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 will provide several characterizations of Walrasian objections and use them to study the bargaining set of the economy, as defined in Mas-Colell (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 and use this result to prove that the bargaining set, the core and the set of competitive allocations are all equivalent solution concepts