The main target of this paper is to investigate the application of Genetic Algorithm (GA) technique in solving the game theory as well as comparing the performance of this technique with linear programming approach in achieving the optimal solution. So, a great attention is focused on the illustration of how to use Genetic Algorithms (GA) techniques in finding the optimal solution of the m x n game. We use GA for solving game theory and find the optimal strategy for player A or player B. Also, we can benefit from the relationship between game theory and the linear programming to find the fitness function and test this fitness function in different examples. After checking the obtained results, we conclude that the proposed methodology of solution based on GA reaches the feasible area reasonably fast and consistently and produces relatively good results. Depending on using GA for solving m x n game, the results show that the optimum solution can be achieved quickly and the solution is almost equal to the analytical one. Nevertheless, on using the (GA) to solve this m x n game, we obtain the result very swiftly.

game theory, genetic algorithms, fitness function, linear programming.