First via a counter example it is shown that the Proposition 3 of Anbarci & Sun (2013) is false. Then a gap and a mistake in their proof are identified. Finally, a modified version of their Proposition 3 is stated and proved.

Core equivalence and shrinking of the core results are well known for economies. The present paper establishes counterparts for bargaining economies, a specific class of production economies (finite and infinite) representing standard two-person bargaining games and their continuum counterparts...

First via a counter example it is shown that Proposition 3 of Anbarci and Sun (2013) is false. Then a gap and a mistake in their proof are identified. Finally, a modified version of their Proposition 3 is stated and proved.