Essays on dynamic information economics

This dissertation studies moral hazard problems and an information acquisition problem in dynamic economic environments. In chapter 1, I study a continuous-time principal-agent model in which a risk-neutral agent protected by limited liability exerts costly efforts to manage a project for her principal. Unobserved risk-taking by the agent is value-reducing in the sense that it increases the chance of large losses, even though it raises short-term profits. In the optimal contract, severe punishment that follows a large loss prevents the agent from taking hidden risks. However, after some histories, punishment can no longer be used because of limited liability. The principal allows the agent to take hidden risk when the firm is close to liquidation. In addition, I explore the roles of standard securities in implementing the optimal contract. The implementation shows that driven by the agency conflicts, incomplete hedging against Poisson risk provides incentives for the agent to take the safe project. Moreover, I study the optimality of "high-water mark" contract widely used in the hedge fund industry and find that "distance-to-threshold" is important in understanding the risk-shifting problem in a dynamic context. In chapter 2, I study a continuous-time moral hazard model in which the principal hires a team of agents to run the business. The firm consists of multiple divisions and agents exert costly efforts to improve the divisional cash flows. The firm size evolves stochastically based on the aggregate cash flows.The model delivers a negative relationship between firm sizes and pay-for-divisional incentives, and I characterize conditions under which joint/relative performance evaluation will be used. I also explore the implications of team production on the firm's optimal capital structure and financial policy. In chapter 3, I study a multi-armed bandits problem with ambiguity. Decision-maker views the probabilities underlying each arm as imprecise and his preference is represented by recursive multiple-priors. I show that the classical "Gittins Index" generalizes to a "Multiple-Priors Gittins Index". In the setting with one safe arm and one ambiguous arm, the decision-maker plays the ambiguous arm if its "Multiple-Priors Gittins Index" is higher than the return delivered by the safe arm. In the multi-armed environment, I obtain the "Multiple-Priors Index Theorem" which states that the optimal strategy for the decision-maker is to play the ambiguous arm with the highest Multiple-Priors Index