We study a two-period moral hazard problem; there are two agents, with action sets that are 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. We introduce and compare three different notions of dynamic worst-case considerations. Within each notion, we define a suitable rule of updating and characterize the principal's optimal payoff guarantee. We find that linear contracts are robustly optimal not only in static settings, but also in dynamic environments with exploration.

This paper studies equilibrium behavior in contests with stochastic progress. Participants have access to a safe action that yields deterministic progress, but they can also take a risky move that stochastically affects their progress towards the goal, and hence 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 expected return of the risky move, the follower takes it in an attempt to catch up. Moreover, if the risky move has a medium return (between high and low), the leader also adopts it when the follower is close to dropping out, reflecting an unexpected preemptive motive. We also analyze how this equilibrium behavior shapes the optimal prize allocation.

This paper 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 quit at any time. The principal knows the reward and provides information over time to motivate effort. We provide a unified framework and derive the optimal information policy in closed form across stationary and nonstationary environments. Within this framework, we identify two precise conditions, each of which guarantees that dynamic disclosure is strictly valuable. First, if the principal is impatient compared to the agent, she prefers the front-loaded effort schedule induced by dynamic disclosure; in a stationary environment, dynamic disclosure is beneficial if and only if the principal is less patient. Second, in an environment where the agent would become pessimistic over time absent any disclosure, dynamic information provision can counteract this downward trend and encourage longer effort. Notably, patience remains a crucial determinant of the structure of the optimal policy.

When a platform is an optional intermediary, should it require price coherence, i.e., that sellers charge the same price to the platform’s users as they charge their direct customers? If the platform does this, how will it affect consumers’ and overall welfare? In a model leveraging insight from the study of third-degree price discrimination, we show that, when demand has flexible curvature, a markup-versus-volume tradeoff arises that governs the platform’s choice. When sellers’ profits are concave enough, the platform prefers to let them charge separate prices. However, when it does require price coherence, there is a drawing-in effect, geared towards low-valuation platform users, which can make this policy surprisingly appealing for consumers.