A network model of manufacturing system is considered. This is a network formation game where players are participants of a production process and their actions are their's requests for interaction. Production networks are formed as a result of an interaction. Players' payoff functions are defined on the set of all possible networks. In this paper the special case of network formation games is considered. Payoff functions are supposed to be additive and depend on subsets of arcs. Two cases are considered. First, subsets of arcs are supposed to be not intersected. The necessary and sufficient conditions for equilibrium are given for this case. The second case is the one where subsets of arcs are determined by 3-agent coalitions. An illustrative example is given where equilibria and a compromise solution are found.