Sequential Linear Contracts on Matroids

2026-02-03

AI Summary

This study addresses the design of linear contracts in sequential action settings under matroid constraints, where an agent sequentially selects actions, observes stochastic rewards, and ultimately submits a matroid-independent set as the basis for the principal’s compensation. The principal incentivizes the agent through a linear sharing mechanism. The authors establish an equivalence between computing the optimal linear contract and the problem of matroid unreliability, constructing a theoretical bridge by introducing parallel element replicas. By integrating tools from matroid theory, stochastic optimization, and contract theory, the paper demonstrates that this equivalence holds for general matroid structures, thereby providing a theoretical foundation for the computability of complex combinatorial contracts.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Cryptocurrency and smart contracts

Abstract

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.

Problem

• sequential contracts
• linear contracts
• matroid constraints
• principal-agent problem
• stochastic rewards

Innovation

• sequential contracts
• linear contracts
• matroid constraints
• principal-agent problem
• matroid unreliability