Validating an agent-based model of the Zipf's Law: A discrete Markov-chain approach

Authored by Bruno Gaujal, Laszlo Gulyas, Yuri Mansury, Eric Thierry

Date Published: 2014-04

DOI: 10.1016/j.jedc.2014.02.002

Sponsors: No sponsors listed

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

This study discusses the validation of an agent-based model of emergent city systems with heterogeneous agents. To this end, it proposes a simplified version of the original agent-based model and subjects it to mathematical analysis. The proposed model is transformed into an analytically tractable discrete Markov model, and its city size distribution is examined. Its discrete nature allows the Markov model to be used to validate the algorithms of computational agent-based models. We show that the Markov chains lead to a power-law distribution when the ranges of migration options are randomly distributed across the agent population. We also identify sufficient conditions under which the Markov chains produce the Zipf's Law, which has never been done within a discrete framework. The conditions under which our simplified model yields the Zipf's Law are in agreement with, and thus validate, the configurations of the original heterogeneous agent-based model. (C) 2014 The Authors. Published by Elsevier B.V.

Tags

Agent-based models Zipf's Law Discrete Markov model