Interacting nonlinear reinforced stochastic processes: Synchronization or non-synchronization. (1st March 2023)

• Record Type: Journal Article
• Authors: Crimaldi, Irene; Louis, Pierre-Yves; Minelli, Ida G.
• Is Part Of: Advances in applied probability. Volume 55:Number 1(2023)
• Page Start: 275
• Page End: 320
• Publication Date: 2023-03-01
• Subjects: Interacting agents -- interacting stochastic processes -- reinforced stochastic process -- urn model -- nonlinear Pólya urn -- generalized Pólya urn -- reinforcement learning -- stochastic approximation -- game theory -- technological dynamics -- CODA models; 60K35 -- 62L20 -- 91D30 -- 60F15 -- 62P20 -- 62P25; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2022.18
• Languages: English
• ISSNs: 0001-8678

Abstract

Abstract: The rich-get-richer rule reinforces actions that have been frequently chosen in the past. What happens to the evolution of individuals' inclinations to choose an action when agents interact? Interaction tends to homogenize, while each individual dynamics tends to reinforce its own position. Interacting stochastic systems of reinforced processes have recently been considered in many papers, in which the asymptotic behavior is proven to exhibit almost sure synchronization. In this paper we consider models where, even if interaction among agents is present, absence of synchronization may happen because of the choice of an individual nonlinear reinforcement. We show how these systems can naturally be considered as models for coordination games or technological or opinion dynamics.