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.

For any abstract bargaining problem a non-cooperative one stage strategic game is constructed whose unique dominant strategies Nash equilibrium implements the Nash solution of the bargaining problem. -- Nash programm ; implementation ; Nash bargaining solution

These notes consist of two parts. In the first one I present a counter example to Proposition 3 of Anbarci & Sun (2013). In the second part I propose a correction based on an axiom similar to one used by Salonen (1988) in the first axomatization of the Discrete Raiffa solution.