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

Author

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  • Gaujal, Bruno
  • Gulyas, Laszlo
  • Mansury, Yuri
  • Thierry, Eric

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.

Suggested Citation

  • Gaujal, Bruno & Gulyas, Laszlo & Mansury, Yuri & Thierry, Eric, 2014. "Validating an agent-based model of the Zipf׳s Law: A discrete Markov-chain approach," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 38-49.
    • Handle: RePEc:eee:dyncon:v:41:y:2014:i:c:p:38-49
    DOI: 10.1016/j.jedc.2014.02.002
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    More about this item

    Keywords

    Discrete Markov model; Agent-based models; Zipf׳s Law;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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