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.
Figures & tables
Figure 1: Agent–environment interaction diagram adapted from [ 16 , 18 ] , illustrating the information flow between agent states, sensing, and action execution within the MAS.
Symbol
Description
Typical Role
αti
Individual ability
dynamic variable
Rti
Percentile rank within team
(0,1]
dts,dtl
Expected dominance
speaker/listener
dt,q
Consensus coefficient
dynamic
rti
Resource share
0–1
Table 1: Model parameters related to the consensus mechanism.
Figure 2: Mean Final Trophic Incoherence across parameter space. Each cell shows the mean final TI across 20 replications. Darker blue tones denote lower TI, indicating stronger hierarchical order.
Figure 3: Variability of TI across replications (IQR). The interquartile range captures cross-run variability for each (c,u) pair. Smaller values indicate greater stability and convergence of hierarchical order.
Figure 4: Phase map of hierarchical regimes. Regions where median(TI)<0.45 and IQR<0.05 are classified as Consistent decrease (dark blue), indicating strong cross-run reproducibility across independent runs; transitional regions as Rebound (orange), and disordered regions as No-change (gray). The map highlights a clear boundary separating ordered and disordered regimes.
Figure 5: Representative trajectories at (c=0.05,u=1.0) . Each gray line represents one of 20 runs; the blue curve is the median TI, and the shaded area the interquartile range (25–75%). The green region highlights periods satisfying the stability criterion ( median(TI)<0.45 and IQR<0.05 ), indicating the onset of a stable hierarchical regime.
Figure 6: Temporal dynamics of TI under varying mutation strengths u . Each curve shows the median TI across 20 replicates (shaded area = IQR 25–75%); rows correspond to different initial heterogeneity c . Higher u values lead to earlier and deeper ordering, whereas low u maintains high-TI, weakly ordered states.
Figure 7: Network Topologies at High and Low TI. (a) Communication network at step 30 000 with F(h)≈0.99 ; (b) at step 30 000 with F(h)≈0.31 . Both are visualized using a trophic-level layout positioning lower-level nodes at the bottom while minimizing edge crossings. Strong hierarchical ordering, as in (b), forms distinct tiers, whereas incoherent networks like (a) appear tangled and symmetric.
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.
This paper develops a general framework for analyzing multi-agent systems with feedback loops between agents actions and collective observations. The framework is built on two fundamental agent-level variables: power, which measures agent influence on collective outcomes, and response functions, which determine how agents react to observations. We derive how macroscopic properties, including total power, useful power, entropy, order, fragility, and mobility, emerge from these two variables of heterogeneous agents. To study the trade off between growth and resilience, we introduce a system-level utility function parameterized by a risk-appetite coefficient and derive an optimal degree of order that balances productivity, stability, and adaptability. The analysis suggests that stronger synchronization can increase collective output but may also increase systemic fragility and reduce mobility. We further argue that order, entropy, information, and useful energy are task-dependent and system-relative concepts whose meanings depend on the objectives of the system. By measuring and designing agent power distributions and response functions, it may be possible to better understand, predict, and optimize collective behavior and identify the conditions under which collective intelligence and optimal order emerge.
Jake J. Xia
Harvard Management Company · Research Affiliate at Massachusetts Institute of Technology
Fei Xiaotong's Differential Order Pattern characterizes rural society as egocentric and relationally graded, with cooperation attenuating over social distance. Although often treated as culturally specific, its mechanistic basis remains under-operationalized, and prior LLM-based simulations have mainly addressed short-term coordination rather than long-horizon social structure. We propose CAREB-MAS, a multi-agent framework grounded in Affect Control Theory, Social Identity Theory, and Durkheimian collective affect. Agents reason through an emotion-ethics-belief chain and maintain dynamically evolving egocentric identities, while the macro environment specifies only individual production, preference-based allocation, and minimal interaction protocols. Across long-horizon simulations, agents spontaneously reproduce five core Differential Order phenomena: stable labor specialization, guanxi-based economic ethics, relational decay of cooperation, emergent relational authority, and clan-based center-periphery stratification. These patterns shift with production structure from kin-centered integration toward greater functional interdependence. Extensive experiment results support interpreting Differential Order as a structure-sensitive emergent outcome of general social mechanisms, with LLM-based multi-agent simulation providing an interdisciplinary framework for studying social structure and change.
Zhiyuan Ji, Xinyu Chen, Ziqi Dai +3
Renmin University of China · Beihang University · Minzu University of China