Provision of Public Goods: Fully Implementing the Core through Private Contributions

Standard economic intuition would say that private provision of public goods will be inefficient due to free-rider problems. This view is in contrast to the results in the literature on full implementation where it is shown that (under certain conditions) games exist which only have efficient equilibria. The games usually used to demonstrate existence are quite complex and seem "unnatural" possibly leading to the perception that implementation requires a central authority to choose and impose the game. In a simple public goods setting, we show that a very natural game—similar to one often used elsewhere in the literature to model private provision—in fact fully implements the core of this economy in undominated perfect equilibria. More specifically, we consider a complete information economy with one private good and two possible social decisions. Agents voluntarily contribute any non-negative amount of the private good they choose and the social decision is to provide the public good iff contributions are sufficient to pay for it. The contributions are refunded otherwise. The set of undominated perfect equilibrium outcomes of this game is exactly the core of the economy. We give some extensions of this result, discuss the role of perfection and alternative equilibrium notions, and discuss the intuition and implications of the results.