We are interested in analyzing the properties of multi-agent systems [13] where a set of agents have to take a decision among two possible alternatives with the help of the social environment or network of the system itself. The ways in which people influence each other through their interactions in a social network and, in particular, the social rules that can be used for the spread of influence have been proposed in an alternative simple game model [11]. However not all individuals play the same role in the process of taking a decision. In this paper we are interested in formalizing and analyzing the simple game model that results in a mediation system. In this scenario we have a social network together with an external participant, the mediator. The mediator can interact, in different degrees, with the agents and thus help to reach a decision.

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