Network Game and Network Formation with Synergy Effect

In this paper we propose a model of network game and network formation with synergy effect where agents form directed-links unilaterally. We study equilibrium strategy and efficient strategy and find some equilibrium strategy. Our first main insight is about the kinds of strategies called as """"the enemy advances I retreat and the enemy retreats I advance"""". Our second result is that more trading is better and the passive trading is better than the active trading.