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lhsi writes:

A mathematical model that looked at the sudden collapse of empires or states was created, with an intent to look at why social disorder can appear from an apparently stable state (an example cited is the Arab Spring in 2011). Factions within a state make choices described by game-theory about whether to accept the political status quo, or to attempt to better their circumstances through costly rebellion.

We find that a small amount of dissatisfaction is typically harmless to the state, but can trigger sudden collapse when there is a sufficient buildup of political inequality. Contrary to intuition, a state is predicted to be least stable when its leadership is at the height of its political power and thus most able to exert its influence through external warfare, lavish expense or autocratic decree.