15. Regime change

Suppose that initially the distribution of wealth is controlled by the rich members of a society. In some periods, the environment is favorable to a successful revolt by the poor. Such a revolt destroys some wealth and makes the remainder permanently available to the poor. If an environment favorable to revolt is rare, the game has a subgame perfect equilibrium in which the rich hand control of the distribution of wealth permanently to the poor (they "democratize") when an environment favorable to revolt occurs. In a model in which the poor members of society need to coordinate for a revolt to succeed, there is an equilibrium in which they coordinate perfectly if they observe the dictator's action, but not if they do not observe that action.