Competition between collective and individual dynamics

TL;DR

This paper presents an exact solution to a segregation model that interpolates between cooperative and individual dynamics, revealing a phase transition from segregation to mixing as cooperativity increases.

Contribution

It introduces a novel analytical approach to link microscopic individual strategies with macroscopic system behavior in social models.

Findings

Increasing cooperativity causes a transition from segregated to mixed phases.

The model demonstrates a shift from low to high utility states.

A simple linking function enables rigorous analysis of strategy-driven dynamics.

Abstract

Linking the microscopic and macroscopic behavior is at the heart of many natural and social sciences. This apparent similarity conceals essential differences across disciplines: while physical particles are assumed to optimize the global energy, economic agents maximize their own utility. Here, we solve exactly a Schelling-like segregation model, which interpolates continuously between cooperative and individual dynamics. We show that increasing the degree of cooperativity induces a qualitative transition from a segregated phase of low utility towards a mixed phase of high utility. By introducing a simple function which links the individual and global levels, we pave the way to a rigorous approach of a wide class of systems, where dynamics is governed by individual strategies.