A Simple Model of Network Formation with Competition Effects

This paper provides a game-theoretic model of network formation with a continuous effort choice. Efforts are strategic complements for direct neighbors in the network and display global substitution/competition effects. We show that if the parameter governing local strategic complements is larger than the one governing global strategic substitutes, then all pairwise Nash equilibrium networks are nested split graphs. We also consider the problem of a planner, who can choose effort levels and place links according to a network cost function. Again all socially optimal configurations are such that the network is a nested split graph. However, the socially optimal network may be different from equilibrium networks and efficient effort levels do not coincide with Nash equilibrium effort levels. In the presence of strategic substitutes, Nash equilibrium effort levels may be too high or too low relative to efficient effort levels. The relevant applications are crime networks and R&D collaborations among firms, but also interbank lending and trade.