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

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 an...

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