Sequential Linear Contracts on Matroids

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.

💡 Research Summary

The paper investigates the design of optimal linear contracts in a principal‑agent setting where the agent’s feasible actions are constrained by a matroid. In this sequential model, the agent may probe elements one by one, paying a known cost for each probe and observing a random value drawn from a discrete distribution. After probing, the agent selects an independent set of the matroid from the observed elements and returns it to the principal. The principal’s reward is the total value of this set, while the contract specifies a payment equal to a fraction α∈