  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.

Optimization and Control;Computer Science and Game Theory