Sequential Contracts
arxiv(2024)
摘要
We study the principal-agent setting, where a principal delegates the
execution of a costly project to an agent. In the classical model, the agent
chooses an action among a set of available actions. Every action is associated
with some cost, and leads to a stochastic outcome for the project. The agent's
action is hidden from the principal, who only observes the outcome. The
principal incentivizes the agent through a payment scheme (a contract) that
maps outcomes to payments, with the objective of finding the optimal contract -
the contract maximizing the principal's expected utility.
In this work, we introduce a sequential variant of the model, capturing many
real-life settings, where the agent engages in multiple attempts, incurring the
sum of costs of the actions taken and being compensated for the best realized
outcome. We study the contract design problem in this new setting. We first
observe that the agent's problem - finding the sequential set of actions that
maximizes his utility for a given contract - is equivalent to the well-known
Pandora's Box problem. With this insight at hand, we provide algorithms and
hardness results for the (principal's) contract design problem, under both
independent and correlated actions. For independent actions, we show that the
optimal linear contract can be computed in polynomial time. Furthermore, this
result extends to the optimal arbitrary contract when the number of outcomes is
a constant. For correlated actions we find that approximating the optimal
contract within any constant ratio is NP-hard.
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