In this work a non-cooperative competitive differential continuous game between an unmanned aerial and an unmanned ground vehicle is studied. Each player acts independently trying to satisfy its own objective function. Specifically the Unmanned Aerial Vehicle (UAV) is trying to reduce the relative distance and orientation by the Unmanned Ground Vehicle (UGV), while the latter is trying to increase it. For this purpose a controller is designed using the concepts of Non-Linear Model Predictive Control (NL-MPC), for each player, to calculate in real time its optimal trajectory by solving its Minimax objective function with double optimization assuming the other player moves optimal (worst case scenario) and taking into account the complete model dynamics. Furthermore, we solve iteratively the above optimization in order to increase the levels of the thinking, making the players more capable of predicting opponent's best move, thus changing their optimal trajectory for their benefit. Various conclusions are made for the strategy that each agent follows in a realistic simulation game of these two 'rational' players, where one player is fast (UAV) and the other is slower (UGV) but more maneuverable.