We propose in this paper a formal framework in which agents arbitrate and play to reach an agreement. The argumentationbased reasoning manages the con icts between arguments having di erent strengths for di erent agents. The argumentative agents justify the hypothesis to which they commit and take into account the commitments of their interlocutors. A third agent is responsible of the nal decision outcome which is taken by resolving the con ict between two players according to their competence.