Essays on experimentation in agency models

This dissertation consists of three chapters in microeconomic theory with a focus on dynamic games and learning. It has applications in political economy, contracts, and industrial organization. In the first chapter, I study censorship in a dynamic game between an informed agent and an uninformed evaluator. Two types of public news are informative about the agents ability -- a conclusive good news process and a bad news process. However, the agent can censor bad news, at some cost, and will censor it if and only if this secures her a significant increase in tenure. Thus, the evaluator faces a bandit problem with an endogenous news process. When bad news is conclusive, the agent always censors when the public belief is sufficiently high, but below a threshold, she either stops censoring or only censors with some probability, depending on the information structure. The possibility of censorship hurts the evaluator and the good agent, and it may also hurt the bad agent. However, when bad news is inconclusive, I show that the good agent censors bad news more aggressively than the bad agent does. This improves the quality of information, and may benefit all players -- the evaluator, the bad agent, and the good agent. The second chapter examines 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. I 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. I 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. In the third chapter, I study how competition between platforms affects the process of social learning. Especially, how product differentiation affects that process. Che and Hörner (2018) show that a monopolistic platform may want to over-recommend consumers in the early phase to gather and learn information for the sake of future consumers. I show that when platforms do not differentiate their products, duopoly competition dramatically reduces the early experimentation, and the Full Transparency policy is the unique equilibrium strategy for both platforms. When platforms differentiate their products, I show that the equilibrium strategy is in between the Full Transparency policy and the optimal policy in the monopolistic case, and depends on how differentiated the products are