Two-stage network formation game with heterogeneous players and private information

We consider a two-stage network formation game with heterogeneous players and private information. The player set consists of a leader and a finite number of other common players, which are divided into two types, passive and positive players. At the first stage, the leader suggests a connected communication network for all players to join. While it is assumed that the link information which every common player receives from the leader is private. Based on the private information, every player chooses the action, accept or reject, at the second stage. A network is formed finally. We show the existence of subgame perfect Nash equilibrium in the game. The result is illustrated by an example.