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Linear Programming by Solving Systems of Differential Equations Using Game Theory

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  • 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

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    File URL: https://mpra.ub.uni-muenchen.de/17191/1/MPRA_paper_17191.pdf
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    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, February.
    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)

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    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

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