Population Uncertainty in Voluntary Contributions of Public Goods

Abstract

I examine how uncertainty in the size of the relevant population affects the voluntary contribution of public goods. I analyze a case where the marginal production of public goods is decreasing and convex, and the agents' social preferences are irrelevant to the population size. In this case, when the number of players is random, the voluntary contribution level in Nash equilibrium is higher than when the number of players is fixed at the mean of the population distribution. I also show that the voluntary contribution level decreases as the expected number of players increases, but such a decreasing tendency is weaker than predicted by the model without population uncertainty. I also analyze another case where the marginal production of public goods is constant and the agents' social preferences are modeled in the form of an increasing concave warm-glow utility in the population size. In this case, the voluntary contribution level is lower under population uncertainty, and the increasing tendency of voluntary contribution level is weaker than predicted by the model without population uncertainty. The results of the lab experiments support many aspects of the theoretical predictions. The linear voluntary contributions mechanism (VCM) experiment can capture the relationships between warm glow and population uncertainty, and the nonlinear VCM experiment can examine whether the contribution level depends on reasoning. As the mean population size increased, the changes in contribution level were smaller under population uncertainty, and the subjects' decisions were determined mainly by the lower bound of the population distribution. When the population distribution was more volatile, subjects contributed more. It is a new observation that the salience of population uncertainty partly drove out warm glow.