A differential game related to terrorism: min-max zero-sum two persons differential game

In this work, we are going to study a differential game related to terrorism: min-max two persons differential game, the question and discuss the qualitative of how best to prosecute the “war on terror” leads to strategic interaction in an inter-temporal setting. We consider a min-max differential game between a governments and a terrorist organization. To obtain the optimal strategy of this problem, we study the analytic form of min-max two persons differential game and a necessary conditions of this problem. Furthermore, we study a saddle point of a min-max differential game. Finally, we make a comparison between the game of the government and the terrorist organization. In the final, I hope from among this study introduce the optimal control and state trajectory to the governments to counter-terrorist.