We examine the nature of contracts that optimally reward innovations in a risky environment, when the innovator is privately informed about the quality of her innovation and must engage an agent to develop it. We model the innovator as a principal who has private but imperfect information about the quality of her project: the project might be worth exploring or not, but even a project of high quality may fail. We characterize the best equilibrium for the high type principal, which is either a separating equilibrium or a pooling one. Due to the interaction between the signaling incentives of the principal and dynamic moral hazard of the agent, the best equilibrium induces inefficiently early termination of the high quality project. The high type principal is forced to share the surplus -- with the agent in the separating equilibrium, or the low type principal in the pooling equilibrium. A mediator, who offers a menu of contracts and keeps the agent uncertain about which contract will be implemented, can increase the payoff of the high type principal to approximate her full information surplus.

We consider social learning in a changing world. With changing states, societies can be responsive only if agents regularly act upon fresh information, which significantly limits the value of observational learning. When the state is close to persistent, a consensus whereby most agents choose the same action typically emerges. However, the consensus action is not perfectly correlated with the state, because societies exhibit inertia following state changes. Phases of inertia may be longer when signals are more precise, even if agents draw large samples of past actions, as actions then become too correlated within samples, thereby reducing informativeness and welfare.

This paper combines dynamic mechanism design with collective experimentation. Agents are heterogeneous in that some stand to benefit from a proposed policy reform, while others are better off under the status quo policy. Each agent's private information regarding her preference type accrues only gradually, over time. A principal seeks a mechanism that maximises the agents' joint welfare, while providing incentives for the agents to truthfully report their gradually acquired, private information. The first-best policy may not be incentive compatible, as uninformed agents may have an incentive to prematurely vote for a policy instead of waiting for their private signal. Under the second-best policy, the principal can incentivise truth-telling by setting a deadline for experimentation, delaying the implementation of the policy reform, and keeping agents in the dark regarding others' reports.