Ciuiu, Daniel (2009): Linear Programming by Solving Systems of Differential Equations Using Game Theory. Published in: Proceedings of the 9th Balkan Conference on Operational Research, September 0206 2009, Constanta, Romania (August 2009): pp. 7278.

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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.
Item Type:  MPRA Paper 

Original Title:  Linear Programming by Solving Systems of Differential Equations Using Game Theory 
Language:  English 
Keywords:  Linear programming, evolutionary game theory, Nash equilibrium. 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C73  Stochastic and Dynamic Games; Evolutionary Games; Repeated Games C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  17191 
Depositing User:  Daniel Ciuiu 
Date Deposited:  09. Sep 2009 07:25 
Last Modified:  11. Feb 2013 23:00 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/17191 