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

• URL: http://arxiv.org/abs/2602.14471v1
• Date: Mon, 16 Feb 2026 05:17:58 GMT
• Title: Socially-Weighted Alignment: A Game-Theoretic Framework for Multi-Agent LLM Systems
• Authors: Furkan Mumcu, Yasin Yilmaz,
• Abstract summary: We propose a game-theoretic framework that modifies inference-time decision making by interpolating between an agent's private objective and an estimate of group welfare.<n>We show that SWA induces a critical threshold $*=(n-)/(n-1)$ above which agents no longer have marginal incentive to increase demand under overload.
• Score: 17.658093330392052
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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 $λ\in[0,1]$. In a shared-resource congestion game with $n$ agents and congestion severity $β$, we show that SWA induces a critical threshold $λ^*=(n-β)/(n-1)$ 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.

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