Voluntary Provision of Public Goods: Experimental Results with Interior Nash Equilibria

Abstract

Introduction The standard public goods experiment involves linear payoffs in which the unique Nash equilibrium is at the lower boundary, i.e. full free riding. Contributions in these experiments tend to decline toward the Nash equilibrium in most treatments, but contributions persist even after as many as 60 rounds. This observation raises the question of whether the persistence of contributions is merely a boundary condition, with residual noise keeping contributions from reaching the Nash equilibrium. In other experimental environments, behavior shows a tendency to differ from boundary equilibria, but is reasonably close to interior predictions (see Smith and Walker, 1993, for examples). One way to address this issue in public goods experiments is to modify the standard linear payoff structure so that the Nash equilibrium is located in the interior of the set of feasible contributions. This paper surveys the evidence from interior-Nash public goods experiments. In some papers, the internal equilibrium is a dominant strategy and in others it is not. The designs also differ in terms of where the equilibrium is located relative to the upper and lower boundaries of the decision space. These relatively new designs are important because they can be used to evaluate the effects of treatment variables (for example, endowments, group size, and information) when the data are not being pulled toward the boundary. In addition, moving the equilibria to the center of the set of feasible contributions tends to reduce or neutralize any bias due to decision errors. Before considering the interior Nash designs, it is useful to review the standard linear structure that produces a boundary equilibrium. An individual i who contributes xi to the public good out of an endowment of E units, thereby consumes E xi units of the private good. If the marginal value of the private good is a constant, v, and the individual's marginal value of total contributions to the public good is also a constant, m, then the individual's earnings are given by:

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