Multiagent Matroid Upgrading: Greedy is Fair and Efficient

2026-05-31

AI Summary

This study addresses the multi-agent matroid upgrading problem, where under the constraint of upgrading at most $k$ elements, each agent must construct a minimum-cost basis in its own matroid. The objective is to minimize a non-decreasing convex function of the agents’ basis costs, thereby jointly optimizing system efficiency and fairness. The work presents the first unified framework that integrates fairness and efficiency in this setting, proposing a greedy-based algorithm that leverages matroid theory, convex optimization, and submodularity analysis for efficient computation. Theoretical analysis establishes the algorithm’s approximation guarantee and fairness properties, while empirical evaluations demonstrate its effectiveness in achieving a balanced trade-off between efficiency and fairness across diverse resource allocation scenarios.

Abstract

This paper introduces a general multiagent matroid upgrading problem that models a broad class of real-world resource allocation tasks. In this setting, there are multiple agents and a ground set of elements, where each element is assigned to a specific agent and has two associated costs: a default cost and a reduced (upgraded) cost. Upgrading an element lowers its cost to the upgraded value, while non-upgraded elements retain their default costs. Each agent is associated with its own matroid, with the goal of finding a minimum-cost basis. The central task is to select at most k elements to upgrade so as to minimize a non-decreasing convex function over the agents' minimum basis costs, capturing both efficiency and fairness objectives in multiagent systems.

Problem

• multiagent
• matroid
• upgrading
• resource allocation
• fairness

Innovation

• multiagent matroid upgrading
• greedy algorithm
• fairness-efficiency tradeoff
• convex cost minimization
• combinatorial optimization