Phase transitions in crowd dynamics of resource allocation

TL;DR

This paper investigates phase transitions in resource allocation processes among agents, revealing a critical point where the system shifts from stable to active, with implications for understanding collective dynamics and non-cooperative behavior.

Contribution

It introduces a new class of resource allocation models exhibiting phase transitions and analyzes their behavior through mean field and numerical methods, connecting to sandpile models.

Findings

Identification of a phase transition from absorbing to active states.

Analytical and numerical agreement on critical exponents.

Discovery of a faster-is-slower effect in the active phase.

Abstract

We define and study a class of resources allocation processes where $gN$ agents, by repeatedly visiting $N$ resources, try to converge to optimal configuration where each resource is occupied by at most one agent. The process exhibits a phase transition, as the density $g$ of agents grows, from an absorbing to an active phase. In the latter, even if the number of resources is in principle enough for all agents ($g<1$), the system never settles to a frozen configuration. We recast these processes in terms of zero-range interacting particles, studying analytically the mean field dynamics and investigating numerically the phase transition in finite dimensions. We find a good agreement with the critical exponents of the stochastic fixed-energy sandpile. The lack of coordination in the active phase also leads to a non-trivial faster-is-slower effect.