Multilateral Ranking Negotiations

In general, negotiations within a group of participants are processes, that starting with participants in some arbitrary (initial) states eventually will achieve an agreement with all participants being in the required negotiated states. Process of negotiation is performed according to a negotiation protocol. Here, an ordering of participants is taken as the negotiation goal; constructing a negotiation protocol for this purpose is referred to as the ranking problem. The formal method used for discussing the considered issue are local computations; in general, they consist in transforming states of the whole structure by way of transforming states of its substructures. The paper aims to discuss communication structures that admit negotiations limited to direct communications between participants of a single ’association’ at a time. Necessary and sufficient conditions for existence of such a ranking protocol for considered structures are formulated and a universal protocol for ranking is given. The paper is a generalization of bilateral negotiations presented in [14], where negotiations are limited to associations containing at most two members; the multilateral protocol presented in this paper covers the case of bilateral negotiations.