We outline a game theoretic model of the decision by political units to pursue independence or accept offers of graded sovereignty from an imperial centre. The key prediction of our model is that geographically extensive, but internally differentiated empires should be common in ‘low-density’ environments where communication and force projection are costly. Smaller, but more internally homogenous states are more likely in ‘high-density’ environments. Our model helps to explain the willingness of many polities in pre-modern periods to accept suzerainty arrangements from imperial cores that had difficulty projecting power. The costs and difficulties of inter-state communication in pre-modern periods made full independence costly and risky and polities more willing to accept limited sovereignty in exchange for imperial ‘protection’. Thus, our model also helps to explain the persistence of geographically extensive empires in eras where the ability to project power was also limited. Key features of the modern era are the declining costs of independent statehood and the increasing ability of states to project power, which helps explain the rise of smaller, less internally differentiated states. We outline the applicability of our model with selected examples from the literature on international state systems and empires.
