Budget-feasible maximum nash social welfare is almost envy-free

Conference item

The Nash social welfare (NSW) is a well-known social welfare measurement that balances individual utilities and the overall efficiency. In the context of fair allocation of indivisible goods, it has been shown by Caragiannis et al. (EC 2016 and TEAC 2019) that an allocation maximizing the NSW is envy-free up to one good (EF1). In this paper, we are interested in the fairness of the NSW in a budget-feasible allocation problem, in which each item has a cost that will be incurred to the agent it is allocated to, and each agent has a budget constraint on the total cost of items she receives. We show that a budget-feasible allocation that maximizes the NSW achieves a 1/4-approximation of EF1 and the approximation ratio is tight. The approximation ratio improves gracefully when the items have small costs compared with the agents' budgets; it converges to 1/2 when the budget-cost ratio approaches infinity.

Authors: Wu, X; Li, B; Gan, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: International Joint Conferences on Artificial Intelligence Organization
• Host title: Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI 2021)
• Publication date: 2021-08-11
• Event title: 30th International Joint Conference on Artificial Intelligence (IJCAI 2021)
• Event location: Online
• Event website: https://ijcai-21.org/
• Event start date: 2021-08-19
• Event end date: 2021-08-27
• DOI: 10.24963/ijcai.2021/65
• Language: English
• Keywords: FFR