Linear contracts are ubiquitous in practice, yet optimal contract theory often prescribes complex, nonlinear structures. We provide a distributional robustness justification for linear contracts. We study a principal-agent problem where the agent exerts costly effort across multiple tasks, generating a stochastic signal upon which the principal conditions payment. The principal faces distributional ambiguity: she knows the expected signal for each effort level, but not the full distribution. She seeks a contract maximizing her worst-case payoff over all distributions consistent with this partial knowledge. Our main result shows that linear contracts are optimal for such a principal. For any contract, there exists a linear contract achieving weakly higher worst-case payoff. The proof introduces the concavification approach built around the notion of self-inducing actions; these are actions where an affine contract simultaneously induces the action as optimal and supports the concave envelope of payments from above. We show that self-inducing actions always exist as maximizers of the gap between the concave envelope and agent's cost function. We extend these results to multi-party settings. In common agency with multiple principals, we show that affine contracts improve all principals' worst-case payoffs. In team production with multiple agents, we establish a complementary necessity result: if any agent's contract is non-affine, the unique ex-post robust equilibrium is zero effort. Finally, we show that homogeneous utility and cost functions yield tractable characterizations, enabling closed-form approximation ratios and a sharp boundary between computational tractability results.

翻译：线性合同在实践中无处不在，然而最优合同理论通常得出复杂非线性结构。本文为线性合同提供了分布稳健性证明。我们研究了一个委托-代理问题，其中代理人投入高成本精力执行多项任务，产生随机信号，委托人据此决定支付。委托人面临分布模糊性：她了解每种努力水平下的期望信号，但不知道完整分布。她寻求在符合这种部分知识的所有分布中最大化最坏情况收益的合同。我们的主要结果表明，线性合同对此类委托人是最优的。对于任意合同，存在一个线性合同能实现不弱的最坏情况收益。证明引入了一种围绕自我诱发行动概念构建的凹化方法；这些行动使得仿射合同既能将该行动诱发生为最优，又能从上方支持支付函数的凹包络。我们证明了自我诱发行动始终作为凹包络与代理人成本函数之差的极大化子存在。我们将这些结果扩展到多方场景。在存在多个委托人的共同代理中，我们证明仿射合同能提升所有委托人的最坏情况收益。在存在多个代理人的团队生产中，我们建立了一个互补的必要性结果：若任何代理人的合同非仿射，则唯一的后验稳健均衡为零努力。最后，我们表明同质效用与成本函数可得出可处理的特征，从而能获得封闭形式的近似比，并界定计算可处理性与不可处理性之间的明确分界。