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

Abstract

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.

Toward a Theory of Charitable Fund‐Raising

“…In general, there will be a continuum of such equilibria. This case is very similar to the ''provision point'' models considered by Bagnoli and Lipman (1989). Typically in these models the public good is provided only at the threshold, not above or below, and any contributions above the threshold are either wasted or refunded in some manner.…”

“…First, notice that this problem is identical to a game in which a group of individuals ᏸ must provide a discrete public good at the level τ k ϩ c(l ). A mechanism suggested by Bagnoli and Lipman (1989) shows that in a simultaneous play game, g i ϭ g * i is an equilibrium. However, g i ϭ 0 is also an equilibrium.…”

Alternative rebate rules in the provision of a threshold public good: An experimental investigation

“…Unfortunately, he does not report differences between the alternate rebate mechanism. Bagnoli and Lipman ( 1989) suggest that rebate policies should have the property that an increase in contribution of$1 by individual i should not generate a refund to individual i of more than $1. All three policies we examine have this property.…”

Self-enforcing norms and efficient non-cooperative collective action in the provision of public goods

“…. , y n ), or the case of a discontinuous public good such that the public good is provided if and only if the sum of contributions exceeds a given threshold as in Bagnoli and Lipman (1989). In some of these cases an efficient non-cooperative outcome exists already if there is no threat of an intra-group conflict.…”