How to fairly allocate resources with Latin Square constraints?
Resource Allocation under the Latin Square Constraint
January 14, 2025
https://arxiv.org/pdf/2501.06506This paper explores the problem of fairly allocating indivisible items (like tasks or resources) among multiple agents over multiple rounds, similar to assigning shifts or scheduling meetings. The allocation follows a "Latin square" constraint, meaning each agent receives each item exactly once, and only one item per round. The research investigates maximizing both total satisfaction (utilitarian social welfare) and minimum individual satisfaction (egalitarian social welfare).
Key points relevant to LLM-based multi-agent systems include:
- Constraint-based allocation: The Latin square constraint provides a structure for agent interaction and resource allocation, relevant to scenarios where agents need to perform diverse tasks or access limited resources in a coordinated manner.
- Optimization of social welfare functions: The focus on utilitarian and egalitarian social welfare reflects the importance of optimizing group performance and individual fairness in multi-agent systems, aligning with goals in collaborative AI. LLMs could potentially be used to model agent preferences and optimize allocations.
- Computational complexity: The research highlights the NP-hardness of finding optimal or even approximately fair allocations, emphasizing the computational challenges of designing efficient allocation mechanisms in complex multi-agent scenarios. This motivates the exploration of heuristics or approximation algorithms that could leverage the power of LLMs for fast, sub-optimal solutions.
- Fairness and efficiency: The analysis of envy-freeness, equitability, and proportionality is relevant to ensuring fair and harmonious collaboration among agents, a crucial factor in building robust and trustworthy multi-agent applications. LLMs can potentially learn fairness criteria and incorporate them into allocation strategies.