Critical Mass: Phase Transitions, Covert Coordination Detection, and Contagion Dynamics in Multi-Agent Systems

Ben Jenkins

Keywords: multi-agent security, phase transitions, collusion detection, partial information decomposition, epidemiological modeling, cascading compromise, percolation theory, LLM agents, adversarial coordination, network topology

TL;DR: We derive critical thresholds for when multi-agent collusion becomes self-sustaining, develop an information-theoretic detector for covert coordination, and model cascading compromise as an epidemic, unifying all three through network structure.

Abstract: As AI agents transition from isolated tools to interacting ecosystems, multi-agent security (MASEC) emerges as a critical and largely uncharted research frontier. We present a unified theoretical framework addressing three fundamental open problems in multi-agent safety. First, we formalize *phase transitions in collusive behavior*, deriving critical thresholds (in terms of agent population size, network density, and communication bandwidth) beyond which coordinated malicious activity becomes self-sustaining. Drawing on statistical mechanics, we show that collusion exhibits a sharp transition analogous to percolation on random graphs and validate this with controlled simulations across heterogeneous agent populations. Second, we develop an *information-theoretic detection framework* for covert inter-agent coordination, extending partial information decomposition of time-delayed mutual information to distinguish benign emergent synergy from adversarial collusion. Third, we introduce an *epidemiological model of cascading agent compromise*, defining a basic reproduction number $\mathcal{R}_0$ for behavioral corruption that propagates through trust networks. We derive closed-form conditions under which a single compromised agent triggers system-wide failure and propose vaccination-inspired intervention strategies. Extensive simulations across network topologies, agent architectures, and adversarial scenarios validate our theoretical predictions and yield actionable deployment guidelines. Our framework provides the first principled foundation for reasoning about when multi-agent systems are safe to deploy and when they are not.

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Submission Number: 233