Modelling and Solving the Problem of Terrorist-Government Conflict Using Differential Games

Terrorism, one of the most trouble-causing issues around the world, by spreading violence and threats tries to achieve its political, ideological, and religious objectives. Analyzing terrorist actions and possible consequences assist researchers to deeply investigate how terrorists make decisions to decrease potential expenses. In this research, to analyze the actions which are taken by each group and also the interaction among them, game theory is employed. Due to the paramount importance of the continuity of time in the real world, differential game model is employed so that accurate results are more possible to achieve. In this research, first, the crucial factors and objectives for both the government and terrorist are modelled. Then the model of the game and Hamilton-Jacobi-Bellman equation are presented. By doing so, military spending and the stock of armaments in equilibrium in Markovian model are analyzed. Finally, the numerical analysis of this model, which shows how they change with respect to these variables, by allotting appropriate amounts to each effective variable in the equilibrium is presented.