| Abstract: |
We study a contract design problem between a principal and multiple agents.
Each agent participates in an independent task with binary outcomes (success
or failure), in which it may exert costly effort towards improving its
probability of success, and the principal has a fixed budget which it can use
to provide outcome-dependent rewards to the agents. Crucially, we assume the
principal cares only about maximizing the agents' probabilities of success,
not how much of the budget it expends. We first show that a contract is
optimal for some objective if and only if it is a successful-get-everything
contract. An immediate consequence of this result is that piece-rate contracts
and bonus-pool contracts are never optimal in this setting. We then show that
for any objective, there is an optimal priority-based weighted contract, which
assigns positive weights and priority levels to the agents, and splits the
budget among the highest-priority successful agents, with each such agent
receiving a fraction of the budget proportional to her weight. This result
provides a significant reduction in the dimensionality of the principal's
optimal contract design problem and gives an interpretable and easily
implementable optimal contract. Finally, we discuss an application of our
results to the design of optimal contracts with two agents and quadratic
costs. In this context, we find that the optimal contract assigns a higher
weight to the agent whose success it values more, irrespective of the
heterogeneity in the agents' cost parameters. This suggests that the structure
of the optimal contract depends primarily on the bias in the principal's
objective and is, to some extent, robust to the heterogeneity in the agents'
cost functions. |