当前位置: X-MOL 学术arXiv.cs.GT › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Competitive Equilibrium For Almost All Incomes: Existence and Fairness
arXiv - CS - Computer Science and Game Theory Pub Date : 2017-05-11 , DOI: arxiv-1705.04212
Erel Segal-Halevi

Competitive equilibrium (CE) is a fundamental concept in market economics. Its efficiency and fairness properties make it particularly appealing as a rule for fair allocation of resources among agents with possibly different entitlements. However, when the resources are indivisible, a CE might not exist even when there is one resource and two agents with equal incomes. Recently, Babaioff and Nisan and Talgam-Cohen (2017) have suggested to consider the entire space of possible incomes, and check whether there exists a competitive equilibrium for almost all income-vectors --- all income-space except a subset of measure zero. They proved various existence and non-existence results, but left open the cases of four goods and three or four agents with monotonically-increasing preferences. This paper proves non-existence in both these cases, thus completing the characterization of CE existence for almost all incomes in the domain of monotonically increasing preferences. Additionally, the paper provides a complete characterization of CE existence in the domain of monotonically decreasing preferences, corresponding to allocation of chores. On the positive side, the paper proves that CE exists for almost all incomes when there are four goods and three agents with additive preferences. The proof uses a new tool for describing a CE, as a subgame-perfect equilibrium of a specific sequential game. The same tool also enables substantially simpler proofs to the cases already proved by Babaioff et al. Additionally, this paper proves several strong fairness properties that are satisfied by any CE allocation, illustrating its usefulness for fair allocation among agents with different entitlements.

中文翻译:

几乎所有收入的竞争均衡:存在与公平

竞争均衡 (CE) 是市场经济学中的一个基本概念。它的效率和公平属性使其作为在可能具有不同权利的代理之间公平分配资源的规则特别有吸引力。然而,当资源不可分割时,即使有一个资源和两个收入相等的代理人,CE 也可能不存在。最近,Babaioff 和 Nisan 和 Talgam-Cohen (2017) 建议考虑可能收入的整个空间,并检查是否存在几乎所有收入向量的竞争均衡——所有收入空间除了测度为零的子集. 他们证明了各种存在和不存在的结果,但留下了具有单调递增偏好的四种商品和三四个代理人的情况。本文证明在这两种情况下都不存在,从而完成了对单调递增偏好领域中几乎所有收入的 CE 存在的表征。此外,该论文提供了在单调递减偏好域中 CE 存在的完整特征,对应于家务分配。从积极的方面来看,本文证明了当有四种商品和三个具有加性偏好的代理时,几乎所有收入都存在 CE。该证明使用了一种新工具来描述 CE,作为特定顺序博弈的子博弈完美均衡。相同的工具还可以对 Babaioff 等人已经证明的案例提供更简单的证明。此外,本文证明了任何 CE 分配都满足的几个强公平属性,
更新日期:2020-10-21
down
wechat
bug