Salesforce Compensation and Two‐Sided Ambiguity: Robust Moral Hazard with Moment Information
研究了企业和销售代理对需求分布信息都有限时的合同设计问题，发现方差信息对最优合同形式（线性或二次）起关键作用，并解释了实践中二次合同的应用。
We analyze a salesforce principal‐agent model where both the firm and sales agent have limited information on the effort‐dependent demand distribution, creating two‐sided ambiguity. Under the max–min decision criteria, the firm offers a contract to the agent who exerts unobservable effort to influence the demand distribution. We formulate the problem as a semi‐infinite program and use the agent's shadow prices to construct the least expensive contract. Next, we use the least expensive contract to create a non‐linear optimization model, which provides the firm's optimal robust contract. Due to the problem's complexity, we focus our attention on the class of distribution‐free contracts. We show that using a distribution‐free contract is a necessary condition for achieving the first‐best outcome. Our analysis reveals that the index of dispersion determines whether the optimal distribution‐free contract is linear or quadratic. Finally, we extend our model to incorporate quota‐bonus contracts and inventory considerations. Overall, our results demonstrate that variance information plays a critical role in designing contracts under distributional ambiguity and provides justification for the application of quadratic contracts in practice.