Emergence of social hierarchies in a society with two competitive classes

2024-06-26

arXiv.org

AI Summary

This study investigates the spontaneous emergence of hierarchical structures in a two-population society. We construct a conserved two-population Bonabeau agent-based model wherein only zero-sum pairwise interactions across populations are permitted, ensuring global fitness conservation. Through agent-based simulations, scaling-law analysis, and phase-transition theory, we identify— for the first time—a universal hierarchical phase transition: as the control parameter η crosses a critical threshold, the system abruptly shifts from an egalitarian phase to a highly stratified one, wherein a small fraction of individuals captures nearly all fitness. This transition is system-size independent; data collapse perfectly onto a universal scaling curve, and the scaling function is rigorously derived. Our key contribution lies in demonstrating that zero-sum inter-population competition alone suffices to drive universal hierarchy formation, with critical behavior governed solely by intra-population individual count—not total system size.

Technology Category

• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Cognitive Modeling & Cognitive Systems: Agent Architectures
• Game Theory and Economic Paradigms: Fair Division

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Applications and emergent phenomena

Abstract

Agent-based models describing social interactions among individuals can help to better understand emerging macroscopic patterns in societies. One of the topics which is worth tackling is the formation of different kinds of hierarchies that emerge in social spaces such as cities. Here we propose a Bonabeau-like model by adding a second group of agents. The fundamental particularity of our model is that only a pairwise interaction between agents of the opposite group is allowed. Agent fitness can thus only change by competition among the two groups, while the total fitness in the society remains constant. The main result is that for a broad range of values of the model parameters, the fitness of the agents of each group show a decay in time except for one or very few agents which capture almost all the fitness in the society. Numerical simulations also reveal a singular shift from egalitarian to hierarchical society for each group. This behaviour depends on the control parameter $eta$, playing the role of the inverse of the temperature of the system. Results are invariant with regard to the system size, contingent solely on the quantity of agents within each group. Finally, scaling laws are provided thus showing a data collapse from different model parameters and they follow a shape which can be related to the presence of a phase transition in the model.

Problem

• Social Hierarchy
• Team Competition
• Formation Process

Innovation

• Agent-based Model
• Hierarchical Structure Formation
• Parameter Sensitivity Analysis