Why, for thousands of years, did "barbarian" societies regularly conquer "civilized" societies with much greater populations and resources? Here's an abstract of a new paper in PLOS ONE:
“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.
Obviously you can set the parameters of a game to make it come out however you want, but I think there is something to this. In a rich, relatively peaceful society, there are many paths to a decent living, and social norms may discourage violence. (Think of Chinese or Egyptian peasants.) To create armies, these societies have to pull men away from productive work, either by compelling service or paying soldiers decent wages. People hate both compulsory military service and high taxes, so either approach generates hatred of the government and possibly unrest and rebellion.
But in a poor society near to a rich one, the opportunity cost of becoming a soldier is much lower, and the potential rewards much greater. In such "barbarian" societies, many more men will be soldiers, even without being paid, so they can field armies as large as those of much bigger states. Soldiering will be a bigger part of their culture, and they will be trained from youth in weapons and battlefield courage, making them most likely better soldiers than the average peasant would be. And if a barbarian leader creates a successful, conquering army, it will rapidly swell as all the young men join for a chance at victory and riches. Hence, Attila or Genghis Khan.
And you just have to love the word Barbarigenesis.