When do Formal Rules and Informal Norms Converge?

We propose evolutionary dynamics to show how rules converge into norms. Individuals play a game of upholding or rejecting a rule, and the more they uphold the rule, the more it becomes established as a norm. We find that when individuals are rational, the initial state determines whether the rule converges into a norm; when individuals are boundedly rational, convergence occurs only if upholding rules is a risk-dominant strategy. This suggests why big-bang reforms that affect only the initial state can fail, while gradualist approaches that can sustain the risk dominance of upholding rules may be more effective.