Online Appendix to “Power-sharing and Leadership Dynamics in Authoritarian Regimes”

Proposition 1: As I argued in the paper, there is no equilibrium in which the dictator uses a pure strategy and the ruling coalition conditions its decision to stage a coup on the observed signal. In any equilibrium in mixed strategies, (i) the ruling coalition stages a coup with probability βθ such that, given the correlation between his actions and the signal θ, the dictator is indifferent between diverting and complying, and (ii) the dictator diverts with probability α such that the ruling coalition is indifferent between staging and not staging a coup after observing a high signal or after observing a low signal, but not both. Note that the ruling coalition cannot be indifferent between staging and not staging a coup after both a high and low signal: If the dictator chooses such α as to make the ruling coalition indifferent between staging and not staging a coup after observing a high signal, than the ruling coalition will prefer not to stage a coup after observing a low signal. Alternatively, if the dictator chooses such α as to make the ruling coalition indifferent between staging and not staging a coup after observing a low signal, than the ruling coalition will prefer to stage a coup after observing a high signal. Thus for the ruling coalition, only the actions (βL = 0, βH > 0) and (βL > 0, βH = 1) can be parts of an equilibrium. To obtain the equilibrium action profile, we solve for the indifference conditions. In the case when (βL = 0, βH > 0), we have