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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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    1. Patryk Siedlecki & Janusz Szwabiński & Tomasz Weron, 2016. "The Interplay Between Conformity and Anticonformity and its Polarizing Effect on Society," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 19(4), pages 1-9.
    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 & Matusik, Milena & Topolski, Krzysztof A., 2024. "Population of entities with three individual states and asymmetric interactions," Applied Mathematics and Computation, Elsevier, vol. 464(C).
    2. 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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