Linear Contracts in Multitasking: Robustness, Uniformity, and Learning (2405.20642v2)

Abstract: In this work, we study the multitasking principal-agent problem. The agent performs several task for the principal, and the principal posts a contract incentivizing the agent to exert effort. The principal can observe a signal for each task, and the contract is a mapping from the space of possible signals to a payment. We study the special class of linear contracts from three perspectives: robustness, uniformity, and learning. Firstly, we show a robustness result: in an ambiguous setting when only first moment information is known, there is a linear contract maximizing the principal's payoff in a worst-case scenario. Secondly, we show a uniformity result: when the agent's cost function is homogeneous to a certain degree and the the principal's utility takes a linear form across tasks, then the optimal contract depends on the agent's cost function only through its homogeneuity degree. Thirdly, we study the problem of learning an optimal linear contract through observational data. We identify this as an measurement error model, and propose instrumental regression methods to estimate the optimal contract parameters in an offline setting, or to learn the optimal contract in an online setting.