Transitions in collective response in multi-agent models of competing populations driven by resource level

TL;DR

This paper investigates how varying resource levels influence collective behavior in multi-agent models, revealing phase transitions and success rate plateaux driven by resource constraints and network interactions.

Contribution

It introduces a detailed analysis of resource-driven phase transitions in a binary-agent-resource model, highlighting self-organized pattern avoidance and the effects of networked versus non-networked agents.

Findings

Success rates form discrete plateaux separated by abrupt transitions.

Increasing resource level restricts the system's exploration of history space.

Networked agents exhibit different dynamics compared to non-networked agents.

Abstract

We aim to study the effects of controlling the resource level in agent-based models. We study, both numerical and analytically, a Binary-Agent-Resource (B-A-R) model in which $N$ agents are competing for resources described by a resource level $1/2 \leq {\cal L} < 1$, where ${\cal L} = L/N$ with $L$ being the maximum amount of resource per turn available to the agents. Each agent picks the momentarily best-performing strategy for decision with the performance of the strategy being a result of the cumulative collective decisions of the agents. The agents may or may not be networked for information sharing. Detailed numerical simulations reveal that the system exhibits well-defined plateaux regions in the success rate which are separated from each other by abrupt transitions. As $L$ increases, the maximum success rate forms a well defined sequence of simple fractions. We analyze the features by studying the outcome time series, the dynamics of the strategies' performance ranking pattern and the dynamics in the history space. While the system tends to explore the whole history space due to its competitive nature, an increasing $L$ has the effect of driving the system to a restricted portion of the history space. Thus the underlying cause of the observed features is an interesting self-organized phenomena in which the system, in response to the global resource level, effectively avoids particular patterns of history outcomes. We also compare results in networked population with those in non-networked population.