Dynamic Collective Action and the Power of Large Numbers
Collective action problems arise when a group's common goal requires costly contributions from sufficiently many members. We study these problems in a dynamic game with privately known participation costs and costly delay. Time creates incentives to postpone contributions, but also allows players to learn from others' actions and coordinate participation. For any discount factor strictly between zero and one, when success requires more than one but fewer than all members of a finite population, every symmetric perfect Bayesian equilibrium has strictly positive probabilities of success and failure, and failure can occur even when every member's contribution cost is below the private benefit of success. In large populations, holding the discount factor fixed, the growth rate of the number of required contributors determines sharply different welfare outcomes. If this number grows more slowly than population size raised to the two-thirds power, there exists a sequence of symmetric equilibria in which success occurs in the first period with probability approaching one and per capita welfare approaches its first-best level. If it grows more quickly than this benchmark, expected utilities converge to zero in every equilibrium, symmetric or asymmetric, and success within any fixed number of periods becomes arbitrarily unlikely.
JEL Classifications: C73, D70, D82, H41
Keywords: Collective Action; Free Riding; War of Attrition; Volunteering}