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 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. We derive the optimal information policy in closed form and thus identify two conditions, each of which guarantees that delayed disclosure is valuable. First, if the principal is impatient compared to the agent, she prefers the front-loaded effort schedule induced by delayed disclosure. In a stationary environment, delayed disclosure is beneficial if and only if the principal is less patient than the agent. Second, if the environment makes the agent become pessimistic over time in absence of any information disclosure, then providing delayed news can counteract this downward trend in the agent's belief and encourage the agent to work longer. Notably, the level of patience remains a crucial determinant of the optimal policy structure.
This paper 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. We also examine the impact of such equilibrium behavior on the optimal prize allocation.
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.