2014/01/01 by Daniele Avitabile, Rebecca Hoyle, Rebecca B. Hoyle +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Bifurcation #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Computer science #Convergence (economics) #Economics #Independent and identically distributed random variables #Jacobian matrix and determinant #Mathematical optimization #Mathematics #Noise (video) #Nonlinear system #Opinion Dynamics and Social Influence #Random variable #Reduction (mathematics) #Scale (ratio) #nlin.PS
paper · pdf · doi:10.1137/140962188
published as SIAM J. Appl. Dyn. Syst., 13(4), 1583-1619, 2014 · This version of the manuscript was accepted for publication on SIADS
openalex publication_date 2014/01/01 · arxiv created 2014/09/03 · arxiv updated 2016/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate coarse equilibrium states of a fine-scale, stochastic, agent-based model of consumer lock-in in a duopolistic market. In the model, agents decide on their next purchase based on a combination of their personal preference and their neighbors' opinions. For agents with independent identically distributed (i.i.d.) parameters and all-to-all coupling, we derive an analytic approximate coarse evolution-map for the expected average purchase. We then study the emergence of coarse fronts when the agents are split into two factions with opposite preferences. We develop a novel Newton--Krylov method that is able to compute accurately and efficiently coarse fixed points when the underlying fine-scale dynamics is stochastic. The main novelty of the algorithm is in the elimination of the noise that is generated when estimating Jacobian-vector products using time-integration of perturbed initial conditions. We present numerical results that demonstrate the convergence properties of the numerical method and use the method to show that macroscopic fronts in this model destabilize at a coarse symmetry-breaking bifurcation.