This paper proposes a Dialectic Analysis Model for Multilateral Argument Games in the open environments, called DAM-MAG, based on dialectic semantics, in terms of the new concept of defensible argument. The DAM-MAG introduces the notion of defensible arguments, and explicitly represents the different internal beliefs of agents and the relations between the "internal beliefs" arguments and the "external" arguments using the dialectic semantics of arguments. This model translates the multilateral argument games into two-party argument games using the ideas from the Arena Contest of Chinese KungFu, to model a dynamic process of finding defensible arguments of the agents who have different claims about the same topic and to form a grid of dialectic analysis trees. This paper provides a novel decision-making support approach which is based on the dialectic semantics for the multi-source information integration.