War, interaction capacity, and the structures of state systems

How have the structures of state systems varied over time and space? We outline a game theoretic model of the decision by political units to accept offers of graded sovereignty from imperial centers. We conceptualize four types of sovereign bargains - tributary, informal extractive, suzerain, and departmental - as a function of whether a polity has external sovereignty and whether resources flow from the subordinate polity to the imperial center through transfers or direct extraction. We then specify the payoffs for these bargains and theorize how increasing interaction capacity and international competition shape the structure of state systems. We show how increasing interaction capacity is related to the transition from transfers to extraction while international competition plays a role only when interaction capacity is already high. We demonstrate the applicability of our model with case studies from low- and high-density environments during the early modern period, respectively: (1) The Oyo Empire of western Africa; (2) Mysore of south Asia.