Dynamic Collective Action and the Power of Large Numbers

Collective action problems arise when a group’s common goal can only be achieved if enough members engage in a costly action. We study the equilibrium properties of such problems when decisions are made dynamically over time, delay is costly, and members have heterogeneous and privately known preferences. In these environments, time acts as both a curse and a blessing: individuals have incentives to delay their actions to observe the commitments of others, yet time can also serve as a coordination device. This tension generates an equilibrium dynamic that combines learning about the eventual probability of success with free-riding incentives and coordination challenges. For finite n, dynamic collective decisions are inherently probabilistic: the probability of success is always positive, but there remains a strictly positive probability that the process halts inefficiently—stopping “cold turkey” before success is achieved. As n becomes large, however, the outcome becomes essentially deterministic: success is achieved either almost instantly at minimum cost or not at all, depending on how quickly the threshold number of participants grows with n. We establish this result by uncovering a novel connection between the equilibria of dynamic Bayesian games and the class of optimal static direct mechanisms requiring Honest and Obedient behavior—an insight that may have broader applicability to mechanism design, beyond collective action environments.