In this work, we study sequential contracts under matroid constraints. In the sequential setting, an agent can take actions one by one. After each action, the agent observes the stochastic value of the action and then decides which action to take next, if any. At the end, the agent decides what subset of taken actions to use for the principal's reward; and the principal receives the total value of this subset as a reward. Taking each action induces a certain cost for the agent. Thus, to motivate the agent to take actions the principal is expected to offer an appropriate contract. A contract describes the payment from the principal to the agent as a function of the principal's reward obtained through the agent's actions. In this work, we concentrate on studying linear contracts, i.e.\ the contracts where the principal transfers a fraction of their total reward to the agent. We assume that the total principal's reward is calculated based on a subset of actions that forms an independent set in a given matroid. We establish a relationship between the problem of finding an optimal linear contract (or computing the corresponding principal's utility) and the so called matroid (un)reliability problem. Generally, the above problems turn out to be equivalent subject to adding parallel copies of elements to the given matroid.

翻译：本研究探讨了在拟阵约束下的序贯合约问题。在序贯设定中，代理人可以逐一采取行动。每次行动后，代理人观察到该行动的随机价值，然后决定是否以及采取何种后续行动。最终，代理人决定将已采取行动中的哪个子集用于委托人的收益；委托人获得该子集的总价值作为回报。代理人采取每个行动都会产生特定成本。因此，为激励代理人采取行动，委托人需提供适当的合约。合约规定了委托人根据代理人行动所获收益向代理人支付的报酬函数。本研究聚焦于线性合约的分析，即委托人将其总收益的固定比例转移给代理人的合约形式。我们假设委托人的总收益基于构成给定拟阵中独立集的行动子集进行计算。我们建立了寻找最优线性合约（或计算相应的委托人效用）问题与所谓的拟阵（不）可靠性问题之间的关联。一般而言，上述问题在向给定拟阵添加元素的平行副本的条件下具有等价性。