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Modeling Asymmetric Interactions in Economy

Author

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  • Mirosław Lachowicz

    (Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland
    The authors contributed equally to this work.)

  • Henryk Leszczyński

    (Institute of Mathematics, University of Gdańsk, ul. Wita Stwosza 57, 80-308 Gdańsk, Poland
    The authors contributed equally to this work.)

Abstract

We consider a general nonlinear kinetic type equation that can describe the time evolution of a variable related to an economical state of an individual agent of the system. We assume asymmetric interactions between the agents. We show that in a corresponding limit, it is asymptotically equivalent to a nonlinear inviscid Burgers type equation.

Suggested Citation

  • Mirosław Lachowicz & Henryk Leszczyński, 2020. "Modeling Asymmetric Interactions in Economy," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:523-:d:340997
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    References listed on IDEAS

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    2. Igor Halperin & Matthew Dixon, 2018. ""Quantum Equilibrium-Disequilibrium": Asset Price Dynamics, Symmetry Breaking, and Defaults as Dissipative Instantons," Papers 1808.03607, arXiv.org, revised May 2019.
    3. George A. Akerlof, 1970. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(3), pages 488-500.
    4. Lachowicz, Mirosław & Leszczyński, Henryk & Topolski, Krzysztof A., 2019. "Self-organization with small range interactions: Equilibria and creation of bipolarity," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 156-166.
    5. Hodges, Stewart & Carverhill, Andrew, 1993. "Quasi Mean Reversion in an Efficient Stock Market: The Characterisation of Economic Equilibria which Support Black-Scholes Option Pricing," Economic Journal, Royal Economic Society, vol. 103(417), pages 395-405, March.
    6. Pareschi, Lorenzo & Toscani, Giuseppe, 2013. "Interacting Multiagent Systems: Kinetic equations and Monte Carlo methods," OUP Catalogue, Oxford University Press, number 9780199655465.
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    Cited by:

    1. Lachowicz, Mirosław & Leszczyński, Henryk & Topolski, Krzysztof A., 2022. "Approximations of kinetic equations of swarm formation: Convergence and exact solutions," Applied Mathematics and Computation, Elsevier, vol. 417(C).

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