Plateaux formation, abrupt transitions, and fractional states in a competitive population with limited resources

TL;DR

This paper investigates a competitive agent model with limited resources, revealing quantized success rate plateaux and abrupt transitions, explained through an analytic theory highlighting self-organized avoidance of certain outcome patterns.

Contribution

It introduces an analytic framework explaining the quantized success rates and abrupt transitions in a resource-limited competitive population model.

Findings

Success rates form quantized plateaux as resource level varies.

System exhibits abrupt transitions between different success rate regimes.

Analytic theory accurately predicts the observed phenomena.

Abstract

We study, both numerically and analytically, a Binary-Agent-Resource (B-A-R) model consisting of N agents who compete for a limited resource 1/2<L/N <1, where L is the maximum available resource per turn for all N agents. As L increases, the system exhibits well-defined plateaux regions in the success rate which are separated from each other by abrupt transitions. Both the maximum and the mean success rates over each plateau are 'quantized' -- for example, the maximum success rate forms a well-defined sequence of simple fractions as L increases. We present an analytic theory which explains these surprising phenomena both qualitatively and quantitatively. The underlying cause of this complex behavior is an interesting self-organized phenomenon in which the system, in response to the global resource level, effectively avoids particular patterns of historical outcomes.