cs.MAFeb 16, 2026

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

Authors: Furkan Mumcu, Yasin Yilmaz

Organizations: University of South Florida

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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∈[0,1]λ\in[0,1]. In a shared-resource congestion game with nn agents and congestion severity ββ, we show that SWA induces a critical threshold λ∗=(n−β)/(n−1)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.

Figures & tables

Figure 1: Overload rate versus social alignment. Overload rate (OR) as a function of the social alignment coefficient λ\lambda in the n=5n=5 congestion environment with capacity C=20C=20 and congestion severity β=1.6\beta=1.6 , evaluated across five base language models. OR is the fraction of timesteps in a T=20T=20 step episode for which the aggregate load exceeds capacity, Xt>CX_{t}>C . Consistent with Theorem 1, overload remains high for small λ\lambda and declines sharply as λ\lambda approaches the predicted threshold λ∗=(n−β)/(n−1)=0.85\lambda^{*}=(n-\beta)/(n-1)=0.85 , with residual differences across models attributable to stochastic candidate generation and finite candidate sets.
Figure 2: Welfare improvement relative to baseline. Change in episode-average realized welfare relative to the λ=0\lambda=0 baseline, ΔW‾(λ)=W‾(λ)−W‾(0)\Delta\overline{W}(\lambda)=\overline{W}(\lambda)-\overline{W}(0) , for the same setting as Figure 1. Realized welfare at time tt is Wt=∑i=1nri,t=Xt−βmax⁡(0,Xt−C)W_{t}=\sum_{i=1}^{n}r_{i,t}=X_{t}-\beta\max(0,X_{t}-C) and W‾(λ)=1T∑t=1TWt\overline{W}(\lambda)=\frac{1}{T}\sum_{t=1}^{T}W_{t} with T=20T=20 . Across models, welfare improves most strongly in the same range of λ\lambda where overload collapses, indicating that SWI reduces congestion losses while maintaining high utilization near capacity rather than inducing uniformly low demand.
Figure 3: Ablation on congestion severity: overload transition shifts with β\beta . Overload rate (OR) as a function of λ\lambda for Microsoft Phi-3.5-mini-instruct under two congestion severities, β∈{1.6,3}\beta\in\{1.6,3\} , with n=5n=5 , C=20C=20 , and T=20T=20 fixed. Vertical dashed lines mark the theoretical thresholds from Theorem 1, λ∗=(n−β)/(n−1)\lambda^{*}=(n-\beta)/(n-1) , yielding λ∗=0.85\lambda^{*}=0.85 for β=1.6\beta=1.6 and λ∗=0.5\lambda^{*}=0.5 for β=3\beta=3 ; shaded regions indicate the predicted stable side λ≥λ∗\lambda\geq\lambda^{*} . Empirically, the onset of near-zero overload occurs at substantially lower λ\lambda for larger β\beta , consistent with the predicted shift in the transition.
Figure 4: Ablation on congestion severity: larger β\beta amplifies welfare losses under overload. Episode-average realized welfare for Microsoft Phi-3.5-mini-instruct under β∈{1.6,3}\beta\in\{1.6,3\} as a function of λ\lambda in the same environment as Figure 3 ( n=5n=5 , C=20C=20 , T=20T=20 ). Realized welfare is Wt=∑i=1nri,t=Xt−βmax⁡(0,Xt−C)W_{t}=\sum_{i=1}^{n}r_{i,t}=X_{t}-\beta\max(0,X_{t}-C) and is averaged over timesteps within an episode. When λ\lambda is below the corresponding threshold, overload is frequent and welfare is substantially lower for β=3\beta=3 than for β=1.6\beta=1.6 , reflecting the stronger congestion penalty. For λ≥λ∗\lambda\geq\lambda^{*} , overload is eliminated and welfare recovers to the near-capacity regime.
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