Linear Programming by Solving Systems of Differential Equations Using Game Theory

Daniel Ciuiu

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Linear programming; evolutionary game theory; Nash equilibrium. (search for similar items in EconPapers)
JEL-codes: C61 C72 C73 (search for similar items in EconPapers)
Date: 2009-06, Revised 2009-06
New Economics Papers: this item is included in nep-gth
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Published in Proceedings of the 9-th Balkan Conference on Operational Research, September 02-06 2009, Constanta, Romania (2009): pp. 72-78

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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:17191

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