Interacting non-linear reinforced stochastic processes: synchronization and no-synchronization

TL;DR

This paper explores how interacting non-linear reinforced stochastic processes can either synchronize or not, depending on reinforcement choices, with implications for modeling coordination, technology, and opinion dynamics.

Contribution

It introduces models where non-linear reinforcement can prevent synchronization despite interaction, expanding understanding of complex stochastic systems.

Findings

Synchronization occurs under certain conditions with linear reinforcement.

Non-linear reinforcement can lead to persistent non-synchronization.

Models are applicable to coordination, technological, and opinion dynamics.

Abstract

'Rich get richer' rule comforts previously often chosen actions. What is happening to the evolution of individual inclinations to choose an action when agents do interact ? Interaction tends to homogenize while each individual dynamics tends to reinforce its own position. Interacting stochastic systems of reinforced processes were recently considered in many papers, where the asymptotic behavior was proven to exhibit a.s. synchronization. We consider in this paper models where, even if interaction among agents is present, absence of synchronization may happen due to the choice of an individual non-linear reinforcement. We show how these systems can naturally be considered as models for coordination games, technological or opinion dynamics.