Private provision of discrete public goods with incomplete information

We analyze the private provision of discrete public good games with incomplete information and continuous contributions. To use the terminology of [Admati and Perry, Review of Economic Studies 58 (1991) 259], we consider contribution and subscription games. In the former, contributions are not refunded if the project is not completed, while in the latter they are. We show that the contribution game has only the strong free riding equilibria if cost is high enough. Thus, in this range of cost, the subscription game is superior to the contribution game. We present several interesting equilibria of both types of games and give a new proof of the ex-post inefficiency of the contribution and the subscription games.