Can three valuation types guarantee EFX?
EFX Exists for Three Types of Agents
This paper explores the "envy-free allocation" problem in distributing items fairly among multiple agents, specifically focusing on the concept of "Envy-Freeness up to any Good" (EFX). The authors prove that an EFX allocation always exists when you have three types of agents with identical preferences within each type.
While the paper doesn't directly deal with LLM-based systems, its key contribution is the exploration of fairness in resource allocation among agents with varying preferences. This is relevant to multi-agent systems where LLMs might need to negotiate and collaborate on tasks or resources while having different goals or priorities. The theoretical framework and algorithms presented could inspire mechanisms for achieving fairer outcomes in such systems.