Maximin Fairness with Mixed Divisible and Indivisible Goods


  • Xiaohui Bei Nanyang Technological University, Singapore
  • Shengxin Liu Harbin Institute of Technology, Shenzhen, China
  • Xinhang Lu Nanyang Technological University, Singapore
  • Hongao Wang Nanyang Technological University, Singapore



Fair Division


We study fair resource allocation when the resources contain a mixture of divisible and indivisible goods, focusing on the well-studied fairness notion of maximin share fairness (MMS). With only indivisible goods, a full MMS allocation may not exist, but a constant multiplicative approximate allocation always does. We analyze how the MMS approximation guarantee would be affected when the resources to be allocated also contain divisible goods. In particular, we show that the worst-case MMS approximation guarantee with mixed goods is no worse than that with only indivisible goods. However, there exist problem instances to which adding some divisible resources would strictly decrease the MMS approximation ratios of the instances. On the algorithmic front, we propose a constructive algorithm that will always produce an \alpha-MMS allocation for any number of agents, where \alpha takes values between 1/2 and 1 and is a monotonically increasing function determined by how agents value the divisible goods relative to their MMS values.




How to Cite

Bei, X., Liu, S., Lu, X., & Wang, H. (2021). Maximin Fairness with Mixed Divisible and Indivisible Goods. Proceedings of the AAAI Conference on Artificial Intelligence, 35(6), 5167-5175.



AAAI Technical Track on Game Theory and Economic Paradigms