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. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    2. 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.
    3. Mateescu, George Daniel, 2006. "Algoritmi genetici de optimizare," Working Papers of Macroeconomic Modelling Seminar 061002, Institute for Economic Forecasting.
    4. Mateescu, George Daniel & Saman, Corina & Buneci, Mihai, 2007. "Algoritmi genetici," Working Papers of Macroeconomic Modelling Seminar 071402, 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. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Nov 2023.
    4. Petrohilos-Andrianos, Yannis & Xepapadeas, Anastasios, 2017. "Resource harvesting regulation and enforcement: An evolutionary approach," Research in Economics, Elsevier, vol. 71(2), pages 236-253.
    5. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    6. Waters, George A., 2009. "Chaos in the cobweb model with a new learning dynamic," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1201-1216, June.
    7. Meng Ding & Hui Zeng, 2022. "Multi-Agent Evolutionary Game in the Recycling Utilization of Sulfate-Rich Wastewater," IJERPH, MDPI, vol. 19(14), pages 1-20, July.
    8. 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.
    9. 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.
    10. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    11. 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.
    12. 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.
    13. Galor, Oded & Klemp, Marc, 2014. "The Biocultural Origins of Human Capital Formation," IZA Discussion Papers 8433, Institute of Labor Economics (IZA).
    14. Moreira, Helmar Nunes & Araujo, Ricardo Azevedo, 2011. "On the existence and the number of limit cycles in evolutionary games," MPRA Paper 33895, University Library of Munich, Germany.
    15. Xie, Yunya & Zhang, Shuhua & Zhang, Zhipeng & Bu, Hongyu, 2020. "Impact of binary social status with hierarchical punishment on the evolution of cooperation in the spatial prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    16. 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.
    17. 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).
    18. Michael Foley & Rory Smead & Patrick Forber & Christoph Riedl, 2021. "Avoiding the bullies: The resilience of cooperation among unequals," PLOS Computational Biology, Public Library of Science, vol. 17(4), pages 1-18, April.
    19. Weibull, Jörgen & Salomonsson, Marcus, 2005. "Natural selection and social preferences," SSE/EFI Working Paper Series in Economics and Finance 588, Stockholm School of Economics, revised 27 Sep 2005.
    20. 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.

    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.