Evolution from political fragmentation to a unified empire in a Malthusian economy

What are the origins of political fragmentation in Europe and political unification in China? This study develops a Malthusian growth model with multiple states to explore interstate competition and the endogenous evolution of human society from political fragmentation to a unified empire. Our model features an agricultural society with citizens and rulers in a Malthusian environment in which the expansion of one state may come at the expense of another state, depending on the elasticity of the land ratio with respect to the ratio of population between states. If this elasticity is less than unity, then multiple states coexist (i.e., political fragmentation) in the long run. However, if this elasticity is equal to unity, then only one state (i.e., political unification) will survive in the long run. Which state becomes the unified empire depends on the state's military power, agricultural productivity, and its rulers' preference for rent-seeking Leviathan taxation. We also discuss the historical relevance of these theoretical predictions.