Essays on Dynamic Games and Mechanism Design

Abstract

This dissertation studies the equilibrium behavior and the design of mechanisms in settings where dynamic considerations are significant features of the environment. The first chapter studies a two-period moral hazard problem; there are two agents, with identical action sets unknown to the principal. The principal contracts with each agent sequentially, and seeks to maximize the worst-case discounted sum of payoffs, where the worst case is over the possible action sets. The principal observes the action chosen by the first agent, and then offers a new contract to the second agent based on this knowledge, thus having the opportunity to explore in the first period. Following nonlinear first-period contracts, optimal second-period contracts may also be nonlinear in some cases. Nonetheless, the analysis shows that linear contracts are optimal in both periods. The second chapter studies the optimal mechanism to motivate effort in a dynamic principal-agent model without transfers. An agent is engaged in a task with uncertain future rewards and can shirk irreversibly at any time. The principal knows the reward of the task and provides information to the agent over time in order to motivate effort. The analysis reveals two key conditions, each of which makes delayed disclosure valuable: one is that the principal is impatient compared to the agent; the other is that the environment makes the agent become pessimistic over time without any information disclosure. The third chapter studies the equilibrium behavior in contests with stochastic progress. Participants have access to a safe action that makes progress deterministically, but they can also take risky moves that stochastically influence their progress towards the goal and thus their relative position. In the unique well-behaved Markov perfect equilibrium of this dynamic contest, the follower drops out if the leader establishes a substantial lead, but resorts to “Hail Marys” beforehand: no matter how low the return of the risky move is, the follower undertakes in an attempt to catch up. Moreover, if the risky move has a medium return (between high and low), the leader will also adopt it when the follower is close to dropping out – an interesting preemptive motive.