Binary participation and incremental provision of public goods

This paper presents a comprehensive analysis of voluntary binary participation in the provision of public goods in a full information setting where the marginal product of participation is positive but decreases with the number of participants. Our study extends Palfrey and Rosenthal's (1984) binary model. It deals with an important special case of uniform multi-person prisoner's dilemma, Schelling (1978), that might be conceived of as the discrete counterpart of the continuous model where both players' contributions and the production function of the public good are continuous, Olson (1965), Chamberlin (1974), McGuire (1974). For pure strategies, we find that as in the continuous setting, Nash equilibria are inefficient and the public good is underprovided. Surprisingly, for mixed strategies, the symmetric equilibria are inefficient, however, even in expected terms, the public good can be overprovided. The concurrence between inefficiency and underprovision of the public good reemerges, provided that one of the following holds: (i) the number of potential participants is sufficiently large, (ii) the marginal product of participation is sufficiently stable, (iii) the costs of participation are sufficiently low or sufficiently high, or (iv) the identical players are constrained to select identical strategies.