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Fair and efficient allocation with few agent types, few item types, or small value levels
Artificial Intelligence ( IF 14.4 ) Pub Date : 2022-11-08 , DOI: 10.1016/j.artint.2022.103820
Trung Thanh Nguyen, Jörg Rothe

In fair division of indivisible goods, allocations that satisfy fairness and efficiency simultaneously are highly desired but may not exist or, even if they do exist, are computationally hard to find. Conditions under which such allocations, or allocations satisfying specific levels of fairness and efficiency simultaneously, can be efficiently found have thus been explored. Following this line of research, this study is concerned with the problem in a high-multiplicity setting where instances come with certain parameters, including agent types, item types, and value levels. Particularly, we address two computational problems. First, we wish to compute fair and Pareto-optimal allocations, w.r.t. any of the common fairness criteria: proportionality, maximin share, and max-min fairness. Second, we seek to find a max-min fair allocation that is efficient in the sense of maximizing utilitarian social welfare. We show that the first problem is tractable for most of the fairness criteria when the number of item types is fixed, or when at least two of the three parameters are fixed. For the second problem, we model it as a bi-criteria optimization problem that is solved approximately by determining an approximate Pareto set of bounded size. Our results are obtained based on dynamic programming and linear programming approaches. Our techniques strengthen known methods and can be potentially applied to other notions of fairness and efficiency.



中文翻译:

代理类型少、项目类型少、价值等级低的公平高效分配

在不可分割商品的公平分配中,同时满足公平和效率的分配是非常需要的,但可能不存在,或者即使它们确实存在,在计算上也很难找到。因此,已经探索了可以有效地找到这种分配或同时满足特定公平和效率水平的分配的条件。在这一系列研究之后,本研究关注高多样性环境中的问题,其中实例带有某些参数,包括代理类型、项目类型和价值水平。特别是,我们解决了两个计算问题。首先,我们希望根据任何常见的公平标准计算公平和帕累托最优分配:比例性、最大份额和最大-最小公平性。第二,我们寻求找到一个最大最小公平分配,在最大化功利社会福利的意义上是有效的。我们表明,当项目类型的数量固定时,或者当三个参数中的至少两个参数固定时,第一个问题对于大多数公平标准都是易于处理的。对于第二个问题,我们将其建模为一个双准则优化问题,通过确定一个有界大小的近似帕累托集来近似求解。我们的结果是基于动态规划和线性规划方法获得的。我们的技术强化了已知的方法,并且可以潜在地应用于其他公平和效率的概念。或者当三个参数中的至少两个是固定的。对于第二个问题,我们将其建模为一个双准则优化问题,通过确定一个有界大小的近似帕累托集来近似求解。我们的结果是基于动态规划和线性规划方法获得的。我们的技术强化了已知的方法,并且可以潜在地应用于其他公平和效率的概念。或者当三个参数中的至少两个是固定的。对于第二个问题,我们将其建模为一个双准则优化问题,通过确定一个有界大小的近似帕累托集来近似求解。我们的结果是基于动态规划和线性规划方法获得的。我们的技术强化了已知的方法,并且可以潜在地应用于其他公平和效率的概念。

更新日期:2022-11-12
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