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Kinetic models of immediate exchange

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  • Els Heinsalu
  • Marco Patriarca

Abstract

We propose a novel kinetic exchange model differing from previous ones in two main aspects. First, the basic dynamics is modified in order to represent economies where immediate wealth exchanges are carried out, instead of reshufflings or uni-directional movements of wealth. Such dynamics produces wealth distributions that describe more faithfully real data at small values of wealth. Secondly, a general probabilistic trading criterion is introduced, so that two economic units can decide independently whether to trade or not depending on their profit. It is found that the type of the equilibrium wealth distribution is the same for a large class of trading criteria formulated in a symmetrical way with respect to the two interacting units. This establishes unexpected links between and provides a microscopic foundations of various kinetic exchange models in which the existence of a saving propensity is postulated. We also study the generalized heterogeneous version of the model in which units use different trading criteria and show that suitable sets of diversified parameter values with a moderate level of heterogeneity can reproduce realistic wealth distributions with a Pareto power law. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Els Heinsalu & Marco Patriarca, 2014. "Kinetic models of immediate exchange," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(8), pages 1-10, August.
    • Handle: RePEc:spr:eurphb:v:87:y:2014:i:8:p:1-10:10.1140/epjb/e2014-50270-6
    DOI: 10.1140/epjb/e2014-50270-6
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    References listed on IDEAS

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    1. Marco Patriarca & Anirban Chakraborti & Kimmo Kaski & Guido Germano, 2005. "Kinetic theory models for the distribution of wealth: power law from overlap of exponentials," Papers physics/0504153, arXiv.org, revised May 2005.
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    Cited by:

    1. Redig, Frank & Sau, Federico, 2017. "Generalized immediate exchange models and their symmetries," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3251-3267.
    2. Kiran Sharma & Anirban Chakraborti, 2016. "Physicists' approach to studying socio-economic inequalities: Can humans be modelled as atoms?," Papers 1606.06051, arXiv.org, revised Aug 2018.
    3. Nicolas Lanchier & Stephanie Reed, 2022. "Distribution of money on connected graphs with multiple banks," Papers 2201.11930, arXiv.org.
    4. Fei Cao & Sebastien Motsch, 2021. "Derivation of wealth distributions from biased exchange of money," Papers 2105.07341, arXiv.org.
    5. Crawford, G. Christopher & Aguinis, Herman & Lichtenstein, Benyamin & Davidsson, Per & McKelvey, Bill, 2015. "Power law distributions in entrepreneurship: Implications for theory and research," Journal of Business Venturing, Elsevier, vol. 30(5), pages 696-713.
    6. Dashti Moghaddam, M. & Mills, Jeffrey & Serota, R.A., 2020. "From a stochastic model of economic exchange to measures of inequality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    7. M. L. Bertotti & G. Modanese, 2016. "Mathematical models describing the effects of different tax evasion behaviors," Papers 1701.02662, arXiv.org.
    8. Guy Katriel, 2014. "The Immediate Exchange model: an analytical investigation," Papers 1409.6646, arXiv.org.
    9. Kemp, Jordan T. & Bettencourt, Luís M.A., 2022. "Statistical dynamics of wealth inequality in stochastic models of growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    10. M. L. Bertotti & G. Modanese, 2018. "Mathematical models describing the effects of different tax evasion behaviors," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 13(2), pages 351-363, July.
    11. Luquini, Evandro & Montagna, Guido & Omar, Nizam, 2020. "Fusing non-conservative kinetic market models and evolutionary computing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

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