Gradual learning from incremental actions

We introduce a collective experimentation problem where a continuum of agents choose the timing of irreversible actions under uncertainty and where public feedback from the actions arrives gradually over time. The leading application is the adoption of new technologies. The socially optimal expansion path entails an informational trade-off where acting today speeds up learning but postponing capitalizes on the option value of waiting. We contrast the social optimum to the decentralized equilibrium where agents ignore the social value of information they generate. We show that the equilibrium can be obtained by assuming that agents ignore the future actions of other agents, which lets us recast the complicated two-dimensional problem as a series of one-dimensional problems.