Fair Division of Mixed Divisible and Indivisible Goods

Xiaohui Bei, Zihao Li, Jinyan Liu, Shengxin Liu, Xinhang Lu
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We study the problem of fair division when the resources contain both divisible and indivisible goods. Classic fairness notions such as envy-freeness (EF) and envy-freeness up to one good (EF1) cannot be directly applied to the mixed goods setting. In this work, we propose a new fairness notion envy-freeness for mixed goods (EFM), which is a direct generalization of both EF and EF1 to the mixed goods setting. We prove that an EFM allocation always exists for any number of agents. We also
more » ... efficient algorithms to compute an EFM allocation for two agents and for n agents with piecewise linear valuations over the divisible goods. Finally, we relax the envy-free requirement, instead asking for ϵ-envy-freeness for mixed goods (ϵ-EFM), and present an algorithm that finds an ϵ-EFM allocation in time polynomial in the number of agents, the number of indivisible goods, and 1/ϵ.
doi:10.1609/aaai.v34i02.5548 fatcat:wf2hgv37wvh2hd7qpoicihpfum