In this paper, we are concerned with an open-loop Nash differential game. We found the necessary conditions for an open loop Nash equilibrium solution and studied the existence for the solution of the dynamical system of the differential game. Also, we used Picard method to find an approximate solution and the uniform convergence is proved. Finally, we constructed figures for the analysis of the differential game. The results can be applied between economic and financial firms as well as industrial firms.
Subject classification: 91A05, 91A10, 91A23, 34A12 and 65L03