IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/17191.html
   My bibliography  Save this paper

Linear Programming by Solving Systems of Differential Equations Using Game Theory

Author

Listed:
  • Ciuiu, Daniel

Abstract

In this paper we will solve some linear programming problems by solving systems of differential equations using game theory. The linear programming problem must be a classical constraints problem or a classical menu problem, i.e. a maximization/minimization problem in the canonical form with all the coefficients (from objective function, constraints matrix and right sides) positive. Firstly we will transform the linear programming problem such that the new problem and its dual have to be solved in order to find the Nash equilibrium of a matriceal game. Next we find the Nash equilibrium by solving a system of differential equations as we know from evolutionary game theory, and we express the solution of the obtained linear programming problem (by the above transformation of the initial problem) using the Nash equilibrium and the corresponding mixed optimal strategies. Finally, we transform the solution of the obtained problem to obtain the solution of the initial problem. We make also a program to implement the algorithm presented in the paper.

Suggested Citation

  • Ciuiu, Daniel, 2009. "Linear Programming by Solving Systems of Differential Equations Using Game Theory," MPRA Paper 17191, University Library of Munich, Germany, revised Jun 2009.
    • Handle: RePEc:pra:mprapa:17191
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/17191/1/MPRA_paper_17191.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mateescu, George Daniel & Saman, Corina & Buneci, Mihai, 2007. "Algoritmi genetici," Working Papers of Macroeconomic Modelling Seminar 071402, Institute for Economic Forecasting.
    2. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    3. Mateescu, George Daniel, 2006. "On the Application of Genetic Algorithms to Differential Equations," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 3(2), pages 5-9, June.
    4. Mateescu, George Daniel, 2006. "Algoritmi genetici de optimizare," Working Papers of Macroeconomic Modelling Seminar 061002, Institute for Economic Forecasting.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dufwenberg, Martin, 1997. "Some relationships between evolutionary stability criteria in games," Economics Letters, Elsevier, vol. 57(1), pages 45-50, November.
    2. Lichi Zhang & Yanyan Jiang & Junmin Wu, 2022. "Evolutionary Game Analysis of Government and Residents’ Participation in Waste Separation Based on Cumulative Prospect Theory," IJERPH, MDPI, vol. 19(21), pages 1-16, November.
    3. Gu, Tianqi & Xu, Weiping & Liang, Hua & He, Qing & Zheng, Nan, 2024. "School bus transport service strategies’ policy-making mechanism – An evolutionary game approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 182(C).
    4. Kulsum, Umma & Alam, Muntasir & Kamrujjaman, Md., 2024. "Modeling and investigating the dilemma of early and delayed vaccination driven by the dynamics of imitation and aspiration," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. Guohui Song & Yongbin Wang, 2021. "Mainstream Value Information Push Strategy on Chinese Aggregation News Platform: Evolution, Modelling and Analysis," Sustainability, MDPI, vol. 13(19), pages 1-17, October.
    6. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    7. Angelo Antoci & Simone Borghesi & Marcello Galeotti, 2013. "Environmental options and technological innovation: an evolutionary game model," Journal of Evolutionary Economics, Springer, vol. 23(2), pages 247-269, April.
    8. Hui Yu & Wei Wang & Baohua Yang & Cunfang Li, 2019. "Evolutionary Game Analysis of the Stress Effect of Cross-Regional Transfer of Resource-Exhausted Enterprises," Complexity, Hindawi, vol. 2019, pages 1-16, November.
    9. Müller, Stephan, 2014. "The evolution of inequality aversion in a simplified game of life," University of Göttingen Working Papers in Economics 219, University of Goettingen, Department of Economics.
    10. Witte, Björn-Christopher, 2012. "Fund managers - Why the best might be the worst: On the evolutionary vigor of risk-seeking behavior," Economics Discussion Papers 2012-20, Kiel Institute for the World Economy (IfW Kiel).
    11. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April.
    12. Wenke Wang & Xiaoqiong You & Kebei Liu & Yenchun Jim Wu & Daming You, 2020. "Implementation of a Multi-Agent Carbon Emission Reduction Strategy under the Chinese Dual Governance System: An Evolutionary Game Theoretical Approach," IJERPH, MDPI, vol. 17(22), pages 1-21, November.
    13. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2023. "Heterogeneous Noise and Stable Miscoordination," Papers 2305.10301, arXiv.org.
    14. Giovanni Ponti, 2000. "Splitting The Baby In Two: How To Solve Solomon'S Dilemma When Agents Are Boundedly Rational," Working Papers. Serie AD 2000-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    15. Antonio E. Bernardo & Ivo Welch, 2001. "On the Evolution of Overconfidence and Entrepreneurs," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 10(3), pages 301-330, September.
    16. Miyaji, Kohei & Tanimoto, Jun, 2021. "The existence of fence-sitters relaxes the spatial prisoner’s dilemma and enhances network reciprocity," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    17. Armando J. Garcia Pires & José Pedro Pontes, 2021. "(De)Industrialization, Technology and Transportation," Open Economies Review, Springer, vol. 32(3), pages 527-538, July.
    18. Gaudeul, Alexia & Keser, Claudia & Müller, Stephan, 2021. "The evolution of morals under indirect reciprocity," Games and Economic Behavior, Elsevier, vol. 126(C), pages 251-277.
    19. Sivan Frenkel & Yuval Heller & Roee Teper, 2018. "The Endowment Effect As Blessing," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(3), pages 1159-1186, August.
    20. Anderhub, Vital & Guth, Werner & Marchand, Nadege, 2004. "Early or late conflict settlement in a variety of games - An experimental study," Journal of Economic Psychology, Elsevier, vol. 25(2), pages 177-194, April.

    More about this item

    Keywords

    Linear programming; evolutionary game theory; Nash equilibrium.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:17191. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.