Under the standard summation technology, pure public goods can be provided via the direct contributions mechanism, even in an arbitrarily large group. However, if the public good exhibits any degree of rivalry, individual consumption of the public good will fall to zero as group size grows large. Thus, the direct contributions mechanism is not robust to the introduction of rivalry. By contrast, Morgan’s (Review of Economic Studies 67:761–784, 2000) lottery mechanism is robust to the introduction of rivalry when the lottery prize is proportional to group size. The lottery mechanism can provide public goods in a large group when the public good exhibits a degree of rivalry, provided that the degree of rivalry is not too high. This suggests that the lottery mechanism can provide a broader range of public goods in a large group than the direct contributions mechanism.
Collective action Public goods Group size Lotteries