RI: Small: The Surprising Power of Sequential Fair Allocation Mechanisms

研究小组将分析在没有货币的市场中进行资源分配的算法，即找到投资于因法律或道德原因而不允许使用货币的领域的机制。例如，大学不会将课程席位出售给出价最高的人，学术同行评审系统也不会根据定价机制指派评审员。在这种情况下，使用集中分配机制来分配资源。为了实用，这些机制需要快速和适应性强。此外，它们必须保证资源得到有效分配(物品流向将从中受益最大的人)和公平(个人和团体不会获得不成比例的小份额利益或承担不公平数量的家务劳动)。研究小组将研究一个简单而有吸引力的范例：顺序分配机制。在顺序分配机制中，用户轮流采取行动(例如，拿走未分配的物品，或从其他人那里偷走物品)，直到满足某些期望的条件(例如，所有物品都已分配)。研究小组将证明，尽管结构简单，但顺序分配机制可以实际用于许多现实世界的问题，同时提供公平和效率保证。研究小组将调查顺序机制提供的保证类型，以及我们可以将它们应用到的领域类型。研究团队将与学术同行审查平台OpenReview、学术会议组织者和大学行政部门合作，测试和实施其发现。大规模资源分配是多智能体系统设计中的一个关键问题。研究人员开发了越来越复杂的算法框架，以确保算法产生既公平又高效的结果。然而，这些算法的复杂性往往阻碍了它们的实际实现，使得它们很难适应特定问题域的需要。为了解决这一缺点，该提案主张采用易于实现和理解的顺序算法技术，而不是复杂的算法框架。该提案审查了顺序分配机制的理论基础及其应用。研究小组将证明，序贯方法提供了显著的计算加速，并通过仔细的分析，保证了公平和效率。对于一般代理偏好，众所周知，实现公平和有效的分配在计算上是困难的；因此，研究团队将专注于特定的代理偏好类，特别关注子模块估值。子模函数自然而然地出现在各种经济领域；然而，它们的结构性质允许我们依赖基本的组合技术，如拟阵优化和图论。该提案将调查挑选序列，最近在OpenReview平台上实现了这一点。该提案还将研究顺序项目转移机制(称为扬基交换机制)，在课程分配等实际领域具有强大的公平和效率保证。最后，该提案将研究一个广泛的顺序框架，以处理更复杂的子模块估值类别，包括家务(如轮班)的公平分配。通过这项提案开发的技术在各种资源分配领域有广泛的应用，例如会议论文审稿人分配、工作轮班分配和课程分配系统。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The research team will analyze algorithms for resource allocation in markets without money, that is, finding mechanisms for investing in domains where the use of money is not allowed for legal or ethical reasons. For example, universities do not sell course seats to the highest bidder, nor do academic peer review systems assign reviewers based on pricing mechanisms. In such cases, centralized allocation mechanisms are used to distribute resources. To be practical, these mechanisms need to be fast and adaptable. In addition, they must guarantee that resources are distributed effectively (items go to those who will benefit most from them) and fairly (individuals and groups do not receive a disproportionately small share of benefits or take on an unfair number of chores). The research team will investigate a simple and appealing paradigm: sequential allocation mechanisms. In a sequential allocation mechanism, users take actions in turns (for example, taking an unassigned item, or stealing an item from someone else), until some desired condition is met (for example, all items have been assigned). The research team will show that despite their simple structure, sequential allocation mechanisms can be practically used in many real-world problems, while offering fairness and efficiency guarantees. The research team will investigate the types of guarantees that sequential mechanisms offer, and the types of domains we can apply them to. The research team will collaborate with OpenReview, an academic peer reviewing platform, academic conference organizers, and with university administration, to test and implement its findings. Large-scale allocation of resources is a key problem in the design of multi-agent systems. Researchers have developed increasingly complex algorithmic frameworks to guarantee that the algorithms produce outcomes that are both fair and efficient. However, the complexity of these algorithms often precludes their practical implementation and makes them difficult to adapt to the needs of specific problem domains. To address this shortcoming, instead of complex algorithmic frameworks, the proposal advocates for sequential algorithmic techniques that are easy to both implement and understand. The proposal examines the theoretical foundations of sequential allocation mechanisms, as well as their applications. The research team will show that the sequential approach offers a significant computational speedup, and via careful analysis, guarantees both fairness and efficiency. For general agent preferences, it is well-known that achieving both fair and efficient allocations is computationally intractable; therefore, the researcher team will focus on specific agent preference classes, with a particular focus on submodular valuations. Submodular functions naturally arise in a variety of economic domains; however, their structural properties allow us to rely on fundamental combinatorial techniques, such as matroid optimization and graph theory. The proposal will investigate picking sequences, with a recent implementation in the OpenReview platform. The proposal will also study sequential item transfer mechanisms (termed Yankee Swap mechanisms), with strong fairness and efficiency guarantees in practical domains, such as course allocation. Finally, the proposal will study a broad sequential framework that handles more complex submodular valuation classes, including the fair allocation of chores (such as work shifts). The techniques developed through this proposal have broad applications in a variety of resource allocation domains, for example, conference paper reviewer assignment, work shift allocation, and course assignment systems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.