In this paper we focus upon a specific process of knowledge sharing, the meaning negotiation one, in presence of a number of negotiating subjects greater than two. Current approaches of the literature are based upon argumentation techniques, persuasion dialogue and game theory and all of them are specific of the negotiation subject and typically limited to two agents. In this paper we present a formalisation of the problem based upon a specific game, the English Auction, that results independent of the number of involved agents and of the negotiation subject. In our framework, each agent's viewpoint is denoted by a logical theory. We show that the problem as posed in the framework is decidable, under a very general assumption and that the computational complexity of the algorithm is polynomial in the number of agents and in the number of preferred representations of the agents.
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