---
title: "A Little Subsidy Ensures MMS Allocation for Three Agents"
authors:
  - "Xiaowei Wu"
  - "Quan Xue"
  - "Shengwei Zhou"
doi: "10.24963/ijcai.2025/454"
url: "https://ijcai.org/proceedings/2025/454"
pdf: "https://ijcai.org/proceedings/2025/0454.pdf"
venue: "Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence"
year: 2025
pages: "4073-4081"
track: "Main Track"
keywords:
  - "Game Theory and Economic Paradigms: GTEP: Computational social choice"
  - "Game Theory and Economic Paradigms: GTEP: Fair division"
---

# A Little Subsidy Ensures MMS Allocation for Three Agents

Xiaowei Wu, Quan Xue, Shengwei Zhou

*Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence*, pages 4073-4081. DOI: [10.24963/ijcai.2025/454](https://doi.org/10.24963/ijcai.2025/454)

## Abstract

We consider the problem of fair allocation of m indivisible items to a group of n agents with subsidies (money). We address scenarios where agents have general additive cost/utility functions. Our work primarily focuses on the special case of three agents. Assuming that the maximum cost/utility of an item to an agent can be compensated by one dollar, we demonstrate that a total subsidy of 1/6 dollars is sufficient to ensure the existence of Maximin Share (MMS) allocations for both goods and chores. Additionally, we provide examples to establish the lower bounds of the required subsidies.