Socially-Weighted Alignment: A Game-Theoretic Framework for Multi-Agent LLM Systems

TL;DR

This paper introduces Socially-Weighted Alignment (SWA), a game-theoretic framework for multi-agent LLM systems that balances individual objectives and group welfare, leading to stable shared-resource management.

Contribution

It proposes SWA as a novel inference-time method to improve multi-agent LLM coordination without retraining or reinforcement learning.

Findings

SWA induces a phase transition at a critical social weight threshold.

Above the threshold, agents stabilize and avoid congestion.

Empirical validation confirms theoretical predictions.

Abstract

Deploying large language model (LLM) agents in shared environments introduces a fundamental tension between individual alignment and collective stability: locally rational decisions can impose negative externalities that degrade system-level performance. We propose Socially-Weighted Alignment (SWA), a game-theoretic framework that modifies inference-time decision making by interpolating between an agent's private objective and an estimate of group welfare via a social weight $\lambda\in[0,1]$. In a shared-resource congestion game with $n$ agents and congestion severity $\beta$, we show that SWA induces a critical threshold $\lambda^*=(n-\beta)/(n-1)$ above which agents no longer have marginal incentive to increase demand under overload, yielding a phase transition from persistent congestion to stable operation near capacity. We further provide an inference-time algorithmic instantiation of SWA that does not require parameter updates or multi-agent reinforcement learning, and use a multi-agent simulation to empirically validate the predicted threshold behavior.