From Cooperation to Hierarchy: A Study of Dynamics of Hierarchy Emergence in a Multi-Agent System

TL;DR

An agent-based model is developed 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, providing a quantitative account of how structured inequality can develop from initially homogeneous populations.

Abstract

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 (7)

• Figure 1: Agent–environment interaction diagram adapted from macal2005tutorialpapasimeon2009modelling, illustrating the information flow between agent states, sensing, and action execution within the MAS.
• 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 $\text{median}(TI) < 0.45$ and $\text{IQR} < 0.05$ 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 ($\text{median}(TI)<0.45$ and $\text{IQR}<0.05$), indicating the onset of a stable hierarchical regime.