Private provision of discrete public goods

We investigate the private provision of a discrete public good. When the size and decomposition of the group are certain, such a problem has, in general, multiple equilibria. Yet, if it is commonly believed that some individuals may be altruists and that the size of the group is a Poisson random variable then equilibrium is unique. If the decomposition uncertainty is very small and the expected group-size sufficiently large then the unique equilibrium is in symmetric mixed strategies. When players’ beliefs about group-size are on average correct, this equilibrium is shown to be very close to the corresponding equilibrium under certainty. This provides a theoretical justification for ignoring the pivotal provision and the zero contributions outcomes, in favour of the symmetric mixed-strategy equilibrium, in sufficiently large discrete public good provision problems. JEL Classification: C72, D70, H41, D89