This polity came into being after the forceful unification of states like Kano and Gobir that had belonged to the confederacy of Hausaland.
the mentioned clues are refinements or extensions of Nash equilibrium theory)  After the passing of its founder, this empire adapted the traditional system of titled offices known as sarauta, though it had initially been prohibited. That founder of this dynasty appointed his brother to rule its twin capital at Gwandu, and himself was a Fulbe scholar of the Qadiriyya brotherhood. This polity came into being after the forceful unification of states like Kano and Gobir that had belonged to the confederacy of Hausaland. Founded after the jihad of the scholar Usman Dan Fodio, a man of the Fulani tribe dubbed "Commander of the Faithful," it was easily the largest post-16th century empire on the African continent. Founded in 1815, FTP, name this caliphate that stretched from modern Burkina Faso to Cameroon.
the mentioned clues are refinements or extensions of Nash equilibrium theory)  
{Sokoto} Caliphate