An optimization formulation to compute Nash equilibrium in finite games

In this paper, we consider a finite n-person non cooperative game. A non-linear optimization model is formulated in a space of dimension equal to sum of the total number of pure strategies in the game and the number of players. A Nash equilibrium of the given game is shown to be equivalent to an optimal solution of the optimization model with zero optimal value. The algorithm is coded in MATLAB using sequential quadratic programming based quasi Newton technique. To make the algorithm user-friendly, a GUI enabled software is developed. Performance of the software is analyzed. Our computational experience has been very satisfactory.