Maybe the last sentence here is wrong?

“Barbarism” is perhaps best understood as a recurring syndrome among peripheral societies in response to the threats and opportunities presented by more developed neighbors. This article develops a mathematical model of barbarigenesis—the formation of “barbarian” societies adjacent to more complex societies—and its consequences, and applies the model to the case of Europe in the first millennium CE. A starting point is a game (developed by Hirshleifer) in which two players allocate their resources either to producing wealth or to fighting over wealth. The paradoxical result is that a richer and potentially more powerful player may lose out to a poorer player, because the opportunity cost of fighting is greater for the former. In a more elaborate spatial model with many players, the outcome is a wealth-power mismatch: central regions have comparatively more wealth than power, peripheral regions have comparatively more power than wealth. In a model of historical dynamics, a wealth-power mismatch generates a long-lasting decline in social complexity, sweeping from more to less developed regions, until wealth and power come to be more closely aligned. This article reviews how well this model fits the historical record of late Antiquity and the early Middle Ages in Europe both quantitatively and qualitatively. The article also considers some of the history left out of the model, and why the model doesn’t apply to the modern world.

That is by Doug Jones, via the excellent Kevin Lewis.