---
title: "Fair Pairwise Exchange among Groups"
authors:
  - "Zhaohong Sun"
  - "Taiki Todo"
  - "Toby Walsh"
doi: "10.24963/ijcai.2021/59"
url: "https://ijcai.org/proceedings/2021/59"
pdf: "https://ijcai.org/proceedings/2021/0059.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "419-425"
track: "Main Track"
keywords:
  - "Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems"
---

# Fair Pairwise Exchange among Groups

Zhaohong Sun, Taiki Todo, Toby Walsh

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 419-425. DOI: [10.24963/ijcai.2021/59](https://doi.org/10.24963/ijcai.2021/59)

## Abstract

We study the pairwise organ exchange problem among groups motivated by real-world applications and consider two types of group formulations. Each
group represents either a certain type of patient-donor pairs who are compatible with the same set of organs, or a set of patient-donor pairs who reside
in the same region. We address a natural research question, which asks how to match a maximum number of pairwise compatible patient-donor
pairs in a fair and individually rational way. We first propose a natural fairness concept that is applicable to both types of group formulations and design
a polynomial-time algorithm that checks whether a matching exists that satisfies optimality, individual rationality, and fairness. We also present several
running time upper bounds for computing such matchings for different graph structures.