On diversifying stable assignments

TL;DR

This paper studies a stable assignment problem with diversifying preferences, proving the uniqueness of the stable assignment and providing a polynomial-time algorithm to find it, which advances understanding of stable matchings with diversification.

Contribution

It introduces a model with diversifying choice functions and proves the existence and uniqueness of the stable assignment, along with an efficient algorithm for computing it.

Findings

Unique stable assignment exists for all inputs.

Polynomial-time algorithm to find the stable assignment.

Model incorporates diversifying preferences in stable assignment.

Abstract

We consider the stable assignment problem on a graph with nonnegative real capacities on the edges and quotas on the vertices, in which the preferences of agents are given via diversifying choice functions. We prove that for any input of the problem, there exists exactly one stable assignment, and propose a polynomial time algorithm to find it.