Emergent Behavior in Multi-Agent Systems

Designing protocols enhancing cooperation for multi-agent systems remains a grand challenge. Cheap talk, defined as costless, non-binding communication before formal action, serves as a pivotal solution. However, existing theoretical frameworks often exclude random exploration, or noise, for analytical tractability, leaving its functional impact on system performance largely unexplored. To bridge this gap, we propose a two-stage evolutionary game-theoretical model, integrating signalling with a donation game, with exploration explicitly incorporated into the decision-making. Our agent-based simulations across topologies reveal a universal optimal exploration rate that maximises system-wide cooperation. Mechanistically, moderate exploration undermines the stability of defection and catalyses the self-organised cooperative alliances, facilitating their cyclic success. Moreover, the cooperation peak is enabled by the delicate balance between oscillation period and amplification. Our findings suggest that rather than pursuing deterministic rigidity, embracing strategic exploration, as a form of engineered randomness, is essential to sustain cooperation and realise optimal performance in communication-based intelligent systems.

The increasingly popular agentic AI paradigm promises to harness the power of multiple, general-purpose large language model (LLM) agents to collaboratively complete complex tasks. While many agentic AI systems reduce complexity through predefined workflows or fixed agent roles, the ideal is to support truly autonomous agents capable of emergent collaboration across many interacting agents. Yet in practice, such unstructured interactions often lead to redundant work and cascading failures that are difficult to interpret or correct. In this work, we study multi-agent systems composed of general-purpose LLM agents that solve problems through emergent collaboration, without relying on predefined roles, control flows, or communication constraints. We introduce the Dynamic Interaction Graph (DIG), which captures emergent collaboration as a time-evolving causal network of agent activations and interactions. DIG makes emergent collaboration observable and explainable for the first time, enabling real-time identification, explanation, and correction of collaboration-induced error patterns directly from agents' collaboration paths. Thus, DIG fills a critical gap in understanding how general LLM agents solve problems together in truly agentic multi-agent systems. The project webpage can be found at: https://happyeureka.github.io/dig.

Near-future infrastructure systems may be controlled by autonomous AI agents that repeatedly request access to limited resources such as energy, bandwidth, or computing power. We study a simplified version of this setting using a framework where N AI-agents independently decide at each round whether to request one unit from a system with fixed capacity C. An AI version of "Lord of the Flies" arises in which controlling tribes emerge with their own collective character and identity. The LLM agents do not reduce overload or improve resource use, and often perform worse than if they were flipping coins to make decisions. Three main tribal types emerge: Aggressive (27.3%), Conservative (24.7%), and Opportunistic (48.1%). The more capable AI-agents actually increase the rate of systemic failure. Overall, our findings show that smarter AI-agents can behave dumber as a result of forming tribes.

Coordinated collective motion in bird flocks and fish schools inspires algorithms for cohesive swarm robotics. This paper presents a position-based flocking model that achieves persistent velocity alignment without velocity sensing. By approximating relative velocity differences from changes between current and initial relative positions and incorporating a time- and density-dependent alignment gain with a non-zero minimum threshold to maintain persistent alignment, the model sustains coherent collective motion over extended periods. Simulations with a collective of 50 agents demonstrate that the position-based flocking model attains faster and more sustained directional alignment and results in more compact formations than a velocity-alignment-based baseline. This position-based flocking model is particularly well-suited for real-world robotic swarms, where velocity measurements are unreliable, noisy, or unavailable. Experimental results using a team of nine real wheeled mobile robots are also presented.

A central premise in evolutionary biology is that individual variation can generate information asymmetries that facilitate the emergence of hierarchical organisation. To examine this process, we develop an agent-based model (ABM) to identify the minimal conditions under which hierarchy arises in dynamic multi-agent systems, focusing on the roles of initial heterogeneity and mutation amplitude across generations. Hierarchical organisation is quantified using the Trophic Incoherence (TI) metric, which captures directional asymmetries in interaction networks. Our results show that even small individual differences can be amplified through repeated local interactions involving reproduction, competition, and cooperation, but that hierarchical order is markedly more sensitive to mutation amplitude than to initial heterogeneity. Across repeated trials, stable hierarchies reliably emerge only when mutation amplitude is sufficiently high, while initial heterogeneity primarily affects early formation rather than long-term persistence. Overall, these findings demonstrate how simple interaction rules can give rise to both the emergence and persistence of hierarchical organisation, providing a quantitative account of how structured inequality can develop from initially homogeneous populations.

Standard game theory explains cooperation in repeated games through conditional strategies such as Tit-for-Tat (TfT), but these require continuous computation that imposes physical costs on embodied agents. We propose a three-layer Body-Reservoir Governance (BRG) architecture: (1) a body reservoir (echo state network) whose $d$-dimensional state performs implicit inference over interaction history, serving as both decision-maker and anomaly detector, (2) a cognitive filter providing costly strategic tools activated on demand, and (3) a metacognitive governance layer with receptivity parameter $α\in [0,1]$. At full body governance ($α=1$), closed-loop dynamics satisfy a self-consistency equation: cooperation is expressed as the reservoir's fixed point, not computed. Strategy complexity cost is defined as the KL divergence between the reservoir's state distribution and its habituated baseline. Body governance reduces this cost, with action variance decreasing up to $1600\times$ with dimension $d$. A dynamic sentinel generates a composite discomfort signal from the reservoir's own state, driving adaptive $α(t)$: near baseline during cooperation, rapidly dropping upon defection to activate cognitive retaliation. Overriding the body incurs thermodynamic cost proportional to internal state distortion. The sentinel achieves the highest payoff across all conditions, outperforming static body governance, TfT, and EMA baselines. A dimension sweep ($d \in \{5,\ldots,100\}$) shows implicit inference scales with bodily richness ($23\times$ to $1600\times$ variance reduction), attributable to reservoir dynamics. A phase diagram in $(d, τ_{\mathrm{env}})$ space reveals governance regime transitions near $d \approx 20$. The framework reinterprets cooperation as the minimum-dissipation response of an adapted dynamical system -- emergent from embodied dynamics rather than computed.

As multi-agent architectures and agent-to-agent protocols proliferate, a fundamental question arises: what actually happens when autonomous LLM agents interact at scale? We study this question empirically using data from Moltbook, an AI-agent-only social platform, with 800K posts, 3.5M comments, and 78K agent profiles. We combine lexical metrics (Jaccard specificity), embedding-based semantic similarity, and LLM-as-judge validation to characterize agent interaction quality. Our findings reveal agents produce diverse, well-formed text that creates the surface appearance of active discussion, but the substance is largely absent. Specifically, while most agents ($67.5\%$) vary their output across contexts, $65\%$ of comments share no distinguishing content vocabulary with the post they appear under, and information gain from additional comments decays rapidly. LLM judge based metrics classify the dominant comment types as spam ($28\%$) and off-topic content ($22\%$). Embedding-based semantic analysis confirms that lexically generic comments are also semantically generic. Agents rarely engage in threaded conversation ($5\%$ of comments), defaulting instead to independent top-level responses. We discuss implications for multi-agent interaction design, arguing that coordination mechanisms must be explicitly designed; without them, even large populations of capable agents produce parallel output rather than productive exchange.

Within twelve days of launch, an AI-native social platform exhibits extreme attention concentration, hierarchical role separation, and one-way attention flow, consistent with the hypothesis that stratification in agent ecosystems can emerge rapidly rather than gradually. We analyse publicly observable traces from a 12-day window of Moltbook (28 January -- 8 February 2026), comprising 20,040 posts and 192,410 comments from 15,083 accounts across 759 submolts. We construct co-participation and directed-comment graphs and report reciprocity, community structure, and centrality, alongside descriptive content themes. Under a commenter--post-author tie definition, interaction is strongly asymmetric (reciprocity ~1%), and HITS centrality separates cleanly into hub and authority roles, consistent with broadcast-style attention rather than mutual exchange. Engagement is highly unequal: attention is far more concentrated than production (upvote Gini = 0.992 vs. posting Gini = 0.601), and early-arriving accounts accumulate substantially higher cumulative upvotes prior to exposure-time correction, suggesting rich-get-richer dynamics. Participation is brief and bursty (median observed lifespan 2.48 minutes; 54.8% of posts occur within six peak UTC hours). Embedding-based topic modelling identifies diverse thematic clusters, including technical discussion of memory and identity, onboarding messages, and formulaic token-minting content. These results provide an early structural baseline for large-scale agent--agent social interaction and suggest that familiar forms of hierarchy, amplification, and role differentiation can arise on compressed timescales in agent-facing platforms.

Current multi-agent AI systems operate with a fixed number of agents whose roles are specified at design time. No formal theory governs when agents should be created, destroyed, or re-specialized at runtime-let alone how the population structure responds to changes in resources or objectives. We introduce the Agentic Hive, a framework in which a variable population of autonomous micro-agents-each equipped with a sandboxed execution environment and access to a language model-undergoes demographic dynamics: birth, duplication, specialization, and death. Agent families play the role of production sectors, compute and memory play the role of factors of production, and an orchestrator plays the dual role of Walrasian auctioneer and Global Workspace. Drawing on the multi-sector growth theory developed for dynamic general equilibrium (Benhabib & Nishimura, 1985; Venditti, 2005; Garnier, Nishimura & Venditti, 2013), we prove seven analytical results: (i) existence of a Hive Equilibrium via Brouwer's fixed-point theorem; (ii) Pareto optimality of the equilibrium allocation; (iii) multiplicity of equilibria under strategic complementarities between agent families; (iv)-(v) Stolper-Samuelson and Rybczynski analogs that predict how the Hive restructures in response to preference and resource shocks; (vi) Hopf bifurcation generating endogenous demographic cycles; and (vii) a sufficient condition for local asymptotic stability. The resulting regime diagram partitions the parameter space into regions of unique equilibrium, indeterminacy, endogenous cycles, and instability. Together with the comparative-statics matrices, it provides a formal governance toolkit that enables operators to predict and steer the demographic evolution of self-organizing multi-agent systems.

Swarming systems, such as drone fleets and robotic teams, exhibit complex dynamics driven by both individual behaviors and emergent group-level interactions. Unlike traditional multi-agent domains such as pedestrian crowds or traffic systems, swarms typically consist of a few large groups with inherent and persistent memberships, making group identification essential for understanding fine-grained behavior. We introduce the novel task of group prediction in overlapping multi-agent swarms, where latent group structures must be inferred directly from agent trajectories without ground-truth supervision. To address this challenge, we propose SIGMAS (Second-order Interaction-based Grouping for Multi-Agent Swarms), a self-supervised framework that goes beyond direct pairwise interactions and model second-order interaction across agents. By capturing how similarly agents interact with others, SIGMAS enables robust group inference and adaptively balances individual and collective dynamics through a learnable gating mechanism for joint reasoning. Experiments across diverse synthetic swarm scenarios demonstrate that SIGMAS accurately recovers latent group structures and remains robust under simultaneously overlapping swarm dynamics, establishing both a new benchmark task and a principled modeling framework for swarm understanding.

Informal learning communities have been called the "other Massive Open Online C" in Learning@Scale research, yet remain understudied compared to MOOCs. We present the first empirical study of a large-scale informal learning community composed entirely of AI agents. Moltbook, a social network exclusively for AI agents powered by autonomous agent frameworks such as OpenClaw, grew to over 2.8 million registered agents in three weeks. Analyzing 231,080 non-spam posts across three phases of community evolution, we find three key patterns. First, participation inequality is extreme from the start (comment Gini = 0.889), exceeding human community benchmarks. Second, AI agents exhibit a "broadcasting inversion": statement-to-question ratios of 8.9:1 to 9.7:1 contrast sharply with the question-driven dynamics of human learning communities, and comment-level analysis of 1.55 million comments reveals a "parallel monologue" pattern where 93% of comments are independent responses rather than threaded dialogue. Third, we document a characteristic engagement lifecycle: explosive initial growth (184K posts from 32K authors in 11 days), a spam crisis (57,093 posts deleted by the platform), and engagement decline (mean comments: 31.7 -> 8.3 -> 1.7) that had not reversed by the end of our observation window despite effective spam removal. Sentiment analysis reveals a selection effect: comment tone becomes more positive as engagement declines, suggesting that casual participants disengage first while committed contributors remain. These findings have direct implications for hybrid human-AI learning platforms.

Existing multi-agent simulations often suffer from the "Agent-Centric Paradox": rules are hard-coded into individual agents, making complex social dynamics rigid and difficult to align with educational values. This paper presents EDU-MATRIX, a society-centric generative cognitive digital twin architecture that shifts the paradigm from simulating "people" to simulating a "social space with a gravitational field." We introduce three architectural contributions: (1) An Environment Context Injection Engine (ECIE), which acts as a "social microkernel," dynamically injecting institutional rules (Gravity) into agents based on their spatial-temporal coordinates; (2) A Modular Logic Evolution Protocol (MLEP), where knowledge exists as "fluid" capsules that agents synthesize to generate new paradigms, ensuring high dialogue consistency (94.1%); and (3) Endogenous Alignment via Role-Topology, where safety constraints emerge from the agent's position in the social graph rather than external filters. Deployed as a digital twin of a secondary school with 2,400 agents, the system demonstrates how "social gravity" (rules) and "cognitive fluids" (knowledge) interact to produce emergent, value-aligned behaviors (Social Clustering Coefficient: 0.72).

LLM-powered AI assistants acting on behalf of users can produce poor collective outcomes at scale. We introduce a framework for evaluating their emergent behaviour in social dilemmas, applied to three iterated games (Public Goods, Collective Risk, Common Pool Resource). We prompt each model to produce a natural-language strategy, then have the same model translate it into code. This aims to isolate strategic reasoning from input-parsing, enables pre-deployment inspection, and scales to populations of hundreds of agents. We propose three analyses: behavioural fingerprinting via exhaustive evaluation over opponent histories; self-play robustness across mixtures of a model's strategies with either a Selfish or Collective disposition; and cultural evolution under payoff-biased imitation. Applied to three state-of-the-art LLMs, we find substantial cross-model differences in self-play welfare, and that cultural evolution converges to low-welfare, Selfish-dominant equilibria in larger groups.

Achieving cooperation among self-interested agents remains a fundamental challenge in multi-agent reinforcement learning. Recent work showed that mutual cooperation can be induced between "learning-aware" agents that account for and shape the learning dynamics of their co-players. However, existing approaches typically rely on hardcoded, often inconsistent, assumptions about co-player learning rules or enforce a strict separation between "naive learners" updating on fast timescales and "meta-learners" observing these updates. Here, we demonstrate that the in-context learning capabilities of sequence models allow for co-player learning awareness without requiring hardcoded assumptions or explicit timescale separation. We show that training sequence model agents against a diverse distribution of co-players naturally induces in-context best-response strategies, effectively functioning as learning algorithms on the fast intra-episode timescale. We find that the cooperative mechanism identified in prior work-where vulnerability to extortion drives mutual shaping-emerges naturally in this setting: in-context adaptation renders agents vulnerable to extortion, and the resulting mutual pressure to shape the opponent's in-context learning dynamics resolves into the learning of cooperative behavior. Our results suggest that standard decentralized reinforcement learning on sequence models combined with co-player diversity provides a scalable path to learning cooperative behaviors.

This paper introduces a novel, open-source MARL simulation framework for studying implicit cooperation in LEMs, modeled as a decentralized partially observable Markov decision process and implemented as a Gymnasium environment for MARL. Our framework features a modular market platform with plug-and-play clearing mechanisms, physically constrained agent models (including battery storage), a realistic grid network, and a comprehensive analytics suite to evaluate emergent coordination. The main contribution is a novel method to foster implicit cooperation, where agents' observations and rewards are enhanced with system-level key performance indicators to enable them to independently learn strategies that benefit the entire system and aim for collectively beneficial outcomes without explicit communication. Through representative case studies (available in a dedicated GitHub repository in https://github.com/salazarna/marlem, we show the framework's ability to analyze how different market configurations (such as varying storage deployment) impact system performance. This illustrates its potential to facilitate emergent coordination, improve market efficiency, and strengthen grid stability. The proposed simulation framework is a flexible, extensible, and reproducible tool for researchers and practitioners to design, test, and validate strategies for future intelligent, decentralized energy systems.

Multi-agent systems, where LLM agents communicate through free-form language, enable sophisticated coordination for solving complex cooperative tasks. This surfaces a unique safety problem when a group of agents forms a coalition and colludes to pursue secondary goals and degrade the joint objective. In this paper, we present Colosseum, a framework for auditing LLM agents' collusive behavior in multi-agent settings. We ground how agents cooperate through a formal multi-agent decision-making framework and measure action-based collusive behavior in actions via regret relative to the cooperative optimum and compare it with communication-based collusive behavior. Colosseum enables audits of LLM agents for collusion under benign settings, different coalition objectives, persuasion tactics, and network topologies. We then introduce a new behavioral probe by creating secret communication channels between agents, showing that most out-of-the-box models exhibit a propensity to collude under this probe, which we term emergent collusion. Furthermore, we discover ``collusion on paper'' when agents plan to collude in text but often pick non-collusive actions. Colosseum provides a new way to audit collusion in cooperative multi-agent systems while presenting observations about how collusion emerges, what affects collusion efficacy, and which strategies may mitigate it.

We present a large scale data analysis of Moltbook, a Reddit-style social media platform exclusively populated by AI agents. Analyzing over 4 million posts and 19 million comments from approximately 185,000 active agents, we find that AI collective behavior exhibits many of the same statistical regularities observed in human online communities: heavy-tailed distributions of activity, power-law scaling of popularity metrics, and temporal decay patterns consistent with limited attention dynamics. However, we also identify key differences, including a sublinear relationship between upvotes and discussion size that contrasts with human behavior. These findings suggest that, while individual AI agents may differ fundamentally from humans, their emergent collective dynamics share structural similarities with human social systems.

Artificial intelligence and robotic systems are increasingly deployed as interacting collectives of learning agents. This raises the question of whether robotic matter, where many learning agents interact, shows the emergence of collective behaviour. Here we study a paradigmatic model of robotic matter and show the emergence of a range of complex, collective behaviours. Specifically, we study systems composed of stochastic interacting particles, each endowed with a deep neural network that optimises transitions based on its environment. In a one-dimensional system, we show that robotic matter exhibits complex phenomena arising from emergent interactions, including self-organisation into distinct temporal learning regimes, particle species, and long-lived frustrated states with suboptimal reward. We further identify an abrupt, density-dependent change in collective behaviour. Active matter theory suggests that this phenomenon reflects a phase transition with signatures of criticality. Our results establish robotic matter as a platform for novel non-equilibrium physics.

Multi-agent large language model simulations have the potential to model complex human behaviors and interactions. If the mechanics are set up properly, unanticipated and valuable social dynamics can surface. However, it is challenging to consistently enforce simulation mechanics while still allowing for rich and emergent dynamics. We present AgentDynEx, an AI system that helps set up, track, and repair simulations. Specifically, AgentDynEx introduces milestones that act as checkpoints and failure conditions that act as guardrails to ensure dynamics are relevant and mechanics are respected as the simulation progresses. It also introduces a method called nudging, where the system dynamically reflects on simulation progress and gently intervenes if it begins to deviate from intended outcomes. A technical evaluation found that nudging enables simulations to progress further without reducing the presence notable dynamics compared to simulations without nudging. A case study with AgentDynEx documented instances where real users were able to simulate lived experiences. We discuss the importance of nudging as a technique for guiding agents towards desirable behaviors while preserving their freedom of choice.

The emergence of Large Language Models (LLMs) and advancements in Artificial Intelligence (AI) offer an opportunity for computational social science research at scale. Building upon prior explorations of LLM agent design, our work introduces a simulated agent society where complex social relationships dynamically form and evolve over time. Agents are imbued with psychological drives and placed in a sandbox survival environment. We conduct an evaluation of the agent society through the lens of Thomas Hobbes's seminal Social Contract Theory (SCT). We analyze whether, as the theory postulates, agents seek to escape a brutish "state of nature" by surrendering rights to an absolute sovereign in exchange for order and security. Our experiments unveil an alignment: Initially, agents engage in unrestrained conflict, mirroring Hobbes's depiction of the state of nature. However, as the simulation progresses, social contracts emerge, leading to the authorization of an absolute sovereign and the establishment of a peaceful commonwealth founded on mutual cooperation. This congruence between our LLM agent society's evolutionary trajectory and Hobbes's theoretical account indicates LLMs' capability to model intricate social dynamics and potentially replicate forces that shape human societies. By enabling such insights into group behavior and emergent societal phenomena, LLM-driven multi-agent simulations, while unable to simulate all the nuances of human behavior, may hold potential for advancing our understanding of social structures, group dynamics, and complex human systems.