Mathematical modeling of Imam Ali ibn Abi Ṭālib’s war strategies with the Khawārij of Nahrawān using game theory

Today, with the advancement of sciences in various fields, mathematics is being optimally used in all sciences, mathematics is therefore widely used in other sciences, and Islamic and military sciences are no exception, and mathematics can be used to design various offensive and defensive operations in battlefields and solve battlefield equations in order to gain absolute or relative superiority over the enemy as in the game theory of war, the application of mathematics can be clearly seen. This practical research, conducted through a library method, has modeled the challenges between the two armies of Imam ʿAlī ibn Abī Ṭālib (AS) and a group called the Māriqīn or Khawārij in the battle of Nahrawān using Game Theory and analyzed each army’s strategies against each other, and finally explore the war utility to find the strategic equilibrium point between them. Therefore, we calculate the utility function for the set of strategies of each of the two armies including the army of Amir alMu’minin, ʿAlī ibn Abī Ṭālib (AS) and the Khawārij of Nahrawān and analyze it.