调整赢家：从分割到销售
Adjusted Winner: from Splitting to Selling
AI总结：
本文提出了一种调整赢家方法的扩展，允许在预算限制下出售资源并重新分配收益，以实现更公平的分配，并通过理论分析和模拟验证了其有效性。
摘要：
调整赢家（AW）方法是用于两个代理人之间公平分配不可分割资源的基本程序。然而，其依赖于资源分割可能导致实际问题。为了解决这一限制，我们提出了一种AW的扩展方法，允许在预算限制下出售选定的资源，随后将所得款项重新分配，从而旨在保持尽可能公平的分配。除了开发这一扩展框架外，我们还提供了公理分析，研究了在我们的设定中公平性和公平感如何被修改。然后，我们正式定义了 resulting 的组合问题，建立了它们的计算复杂性，并设计了一个完全多项式时间近似方案（FPTAS）来缓解其内在的不可行性。最后，我们用计算机模拟补充了我们的理论结果。
英文摘要：
The Adjusted Winner (AW) method is a fundamental procedure for the fair division of indivisible resources between two agents. However, its reliance on splitting resources can lead to practical complications. To address this limitation, we propose an extension of AW that allows the sale of selected resources under a budget constraint, with the proceeds subsequently redistributed, thereby aiming for allocations that remain as equitable as possible. Alongside developing this extended framework, we provide an axiomatic analysis that examines how equitability and envy-freeness are modified in our setting. We then formally define the resulting combinatorial problems, establish their computational complexity, and design a fully polynomial-time approximation scheme (FPTAS) to mitigate their inherent intractability. Finally, we complement our theoretical results with computer-based simulations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
