Freedom to Not Join: A Voluntary Participation Game of a Discrete Public Good

A problem of the provision of a discrete public good is considered. All members in the society are homogeneous and they decide simultaneously whether to contribute to the provision. Contribution cost per person is …xed and non-refundable. Because of the free-rider problem, ine¢ ciency in the provision is inevitable, even in the most e¢ cient symmetric Nash equilibrium. However, when we add a pre-stage game where all members decides simultaneously whether to voluntarily participate to the original contribution game, expected social welfare might be improved in the symmetric subgame perfect equilibrium. It turns out that the improvement is always possible when the cost of contribution is su¢ ciently high.