Aspiring autocrats often rally citizens' support to dismantle democratic institutions. One widely used instrument is the strongman narrative (SN): a strong leader can improve economic performance. In this paper, we build a behavioral game-theoretic model using Bayesian networks to study the effectiveness of the SN. We find that believing in the SN increases support for the leader, but the extent to which it does depends on the polity’s history. In particular, we find a form of historical complementarity or “authoritarian legacy:” past support for authoritarian leaders increases the citizen’s incentives to support the leader today. Leader valence plays a complicated role: for intermediate values, there are multiple equilibria that differ in support while leaders with higher valence have stronger incentives to propagate the SN when it is incorrect. We also extend our model to study the role of repression and economic shocks on the effectiveness of the SN.