The dynamics of repression in dictatorships

We study the optimal strategy for a dictator hanging onto power by choosing how much repression to apply in every period. State variables are the amount of “hate” and “fear” in society which are both increasing in the amount of repression from the previous period. Hate, fear and a random shock, determine the quantity of repression required for the dictator to survive period t. We show under certain conditions that in every period there are only two possible optimal choices: the minimal repression necessary to retain power (“No Demonstration”) or the maximum possible repression (“Demonstration”). When Demonstration is optimal it will remain optimal after fear is reduced and when No Demonstration is optimal it will remain
optimal when fear is increased.