Equilibrium in a network game with production and knowledge externalities

In each node of network, economy is described by the simple two-period Romer's model of endogenous growth with production and knowledge externalities. The sum of knowledge levels in the neighbor nodes causes an externality in the production of each node of network. The game equilibrium in the network is investigated. The agents' solutions in dependence on the size of externality are obtained. The uniqueness of inner equilibrium is proved. The role of passive agents in network formation is studied; in particular, the possibilities of adding of a passive agent to a regular network, and also of joining of regular networks through nodes with passive agents. It is shown, that the sum of knowledge levels in all the nodes decreases under adding of a new link.