Noise Reduction in Coarse Bifurcation Analysis of Stochastic Agent-Based Models: An Example of Consumer Lock-In

Authored by Daniele Avitabile, Rebecca Hoyle, Giovanni Samaey

Date Published: 2014

DOI: 10.1137/140962188

Sponsors: Flanders Research Foundation Belgian Federal Science Policy Office (BELSPO)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

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.

Tags

Simulation Agent-based models individual-based models Evolution behavior Opinion formation Dynamics networks collective motion equation-free methods multiple-scale analysis Computational approach Grained analysis