The efficiency of individual optimization in the conditions of competitive growth

TL;DR

This paper investigates a multi-agent model of competitive growth, analyzing how individual optimization affects system dynamics, phase transitions, and mass distribution behaviors near critical points.

Contribution

It introduces a multi-agent model incorporating individual optimization and analyzes phase diagrams and power-law behaviors in competitive growth.

Findings

Identification of high and low competition phases separated by a critical point

Revealed anomalies in optimization efficiency near the critical regime

Power-law behavior observed in mass distributions at criticality

Abstract

The paper aims to discuss statistical properties of the multi-agent based model of competitive growth. Each of the agents is described by growth (or decay) rule of its virtual "mass" with the rate affected by the interaction with other agents. The interaction depends on the strategy vector and mutual distance between agents and both are subjected to the agent's individual optimization process. Steady-state simulations yield phase diagrams with the high and low competition phases (HCP and LCP, respectively) separated by critical point. Particular focus has been made on the indicators of the power-law behavior of the mass distributions with respect to the critical regime. In this regime the study has revealed remarkable anomaly in the optimization efficiency.