Learning in mis-specified models and the possibility of cycles

I study the problem of a monopolist maximizing a sum of discounted profits facing a linear demand curve whose slope and intercept are unknown. I show that if the monopolist has a mis-specified model, i.e., if the true slope and intercept lie outside of the support of the monopolist's prior beliefs, then actions and beliefs may cycle on every sample path. This behavior is shown to be robust to perturbations in the prior, true parameter, and actions. Such behavior is not possible if the agent's model is correctly specified; instead actions and beliefs necessarily converge.