The assignment problem has a wide variety of applications and in particular, it can be applied to any two-sided market. In this paper, we propose a multi-agent framework to distributively solve this kind of assignment problems, by providing agents which negotiate with respect to their preferences. We present here a realisation of the minimal concession strategy. Our realisation of the minimal concession strategy has useful properties: it preserves the privacy and improves the optimality of the solution and the equity amongst the partners.