J. Garg, Patricia C. McGlaughlin, Martin Hoefer, M. Schmalhofer
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引用次数: 0
Abstract
We study markets with mixed manna, where m divisible goods and chores shall be divided among n agents to obtain a competitive equilibrium. Equilibrium allocations are known to satisfy many fairness and efficiency conditions. While a lot of recent work in fair division is restricted to linear utilities and chores, we focus on a substantial generalization to separable piecewise-linear and concave (SPLC) utilities and mixed manna. We first derive polynomial-time algorithms for markets with a constant number of items or a constant number of agents. Our main result is a polynomial-time algorithm for instances with a constant number of chores (as well as any number of goods and agents) under the condition that chores dominate the utility of the agents. Interestingly, this stands in contrast to the case when the goods dominate the agents utility in equilibrium, where the problem is known to be PPAD-hard even without chores.
我们研究的是混合甘露市场，其中 m 种可分割商品和家务应在 n 个代理人之间进行分配，以获得竞争性均衡。众所周知，均衡分配满足许多公平和效率条件。最近很多关于公平分配的研究都局限于线性效用和家务，而我们则专注于对可分离的片状线性凹（SPLC）效用和混合甘露的实质性推广。我们首先推导了具有恒定项目数或恒定代理数的市场的多项式时间算法。我们的主要结果是，在家务活支配代理人效用的条件下，对于家务活数量不变的实例（以及任何数量的物品和代理人）的多项式时间算法。有趣的是，这与商品在均衡状态下支配代理人效用的情况形成了鲜明对比，在这种情况下，即使没有家务活，问题也是已知的 PPAD 难。
期刊介绍：
JAIR(ISSN 1076 - 9757) covers all areas of artificial intelligence (AI), publishing refereed research articles, survey articles, and technical notes. Established in 1993 as one of the first electronic scientific journals, JAIR is indexed by INSPEC, Science Citation Index, and MathSciNet. JAIR reviews papers within approximately three months of submission and publishes accepted articles on the internet immediately upon receiving the final versions. JAIR articles are published for free distribution on the internet by the AI Access Foundation, and for purchase in bound volumes by AAAI Press.
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