A binary public good is a type of public good for which provision is a binary outcome and only occurs if the total amount of contributions received exceeds some threshold level. This thesis is concerned with the private provision of a binary public good by means of voluntary contributions. In the seminal paper by Palfrey and Rosenthal (1984), this problem is modelled as a non-cooperative game, in which players can contribute either a fixed amount or nothing at all towards the provision of a binary public good. They show that there are both efficient and inefficient equilibria in terms of binary public good provision. This contrasts with continuous public goods, for which voluntary provision is always inefficient.
The main objective of this thesis is to extend the existing game theoretic literature on voluntary provision of binary public goods. It examines the effects of an increase in the cost of contributing and the effects of group size uncertainty on the outcomes of a non-cooperative game. It also investigates the optimal sample design for assessing the likelihood of provision on the basis of a sample.
The first contribution of the thesis shows that an increase in the cost of contributing generally reduces the equilibrium contribution rate and the probability of provision. Furthermore, it illustrates that group size uncertainty leads to stronger free-riding and a lower probability of provision than when the total number of players is certain. This contribution employs the Poisson games approach developed by Myerson (1998, 2000) to capture group size uncertainty in the game.
Since the provision of the public good depends on the number of potential contributors canvassed, the second contribution of the thesis examines the use of sample design as a means of improving the likelihood of provision. It employs statistical power analysis as a guide to determining the optimal design of sample games for binary public good provision. The equilibrium probability of provision for these sample games is decreasing with the size of the sample, which suggests that the inferred likelihood of provision may be improved by reducing the sample size. This result indicates that the optimal sample design, whether for a public good game, an election poll, or an economic experiment, may need to account for the strategic interaction of sample size with equilibrium behaviour in voluntary participation problems.