We consider a (pure) public goods provision problem with voluntary participation in a quasi-linear economy. We propose a new hybrid solution concept, the free-riding-proof core (FRP-Core), which endogenously determines a contribution group, public good provision level, and its cost-sharing. The FRP-Core is always nonempty in public good economies but does not usually achieve global efficiency. The FRP-Core has support from both cooperative and noncooperative games. In particular, it is equivalent to the set of perfectly coalition-proof Nash equilibrium (Bernheim, Peleg, and Whinston, 1987) of a dynamic game with players' participation decisions followed by a common agency game of public goods provision. We illustrate various properties of the FRPCore with an example. We also show that the equilibrium level of public good shrinks to zero as the economy is replicated.