Sector of Industrial Management and Operational Research, School of Mechanical Engineering, National Technical University of Athens, Athens, Greece.
PLoS One. 2012;7(9):e44535. doi: 10.1371/journal.pone.0044535. Epub 2012 Sep 14.
The fair division of a surplus is one of the most widely examined problems. This paper focuses on bargaining problems with fixed disagreement payoffs where risk-neutral agents have reached an agreement that is the Nash-bargaining solution (NBS). We consider a stochastic environment, in which the overall return consists of multiple pies with uncertain sizes and we examine how these pies can be allocated with fairness among agents. Specifically, fairness is based on the Aristotle's maxim: "equals should be treated equally and unequals unequally, in proportion to the relevant inequality". In this context, fairness is achieved when all the individual stochastic surplus shares which are allocated to agents are distributed in proportion to the NBS. We introduce a novel algorithm, which can be used to compute the ratio of each pie that should be allocated to each agent, in order to ensure fairness within a symmetric or asymmetric NBS.
剩余的公平分配是最广泛研究的问题之一。本文侧重于具有固定分歧支付的讨价还价问题，其中风险中性的代理人已经达成了纳什讨价还价解决方案（NBS）的协议。我们考虑了一个随机环境，其中整体回报由多个不确定大小的馅饼组成，我们研究如何在代理人之间公平地分配这些馅饼。具体而言，公平是基于亚里士多德的格言：“平等的人应该平等对待，不平等的人应该按照相关的不平等程度不平等对待”。在这种情况下，当分配给代理人的所有单个随机剩余份额都按照 NBS 成比例分配时，就实现了公平。我们引入了一种新的算法，该算法可用于计算应分配给每个代理人的每个馅饼的比例，以确保在对称或不对称的 NBS 中实现公平。
