Many interactive intelligent systems, such as recommendation and information retrieval systems, treat users as a passive data source. Yet, users form mental models of systems and instead of passively providing feedback to the queries of the system, they will strategically plan their actions within the constraints of the mental model to steer the system and achieve their goals faster. We propose to explicitly account for the user's theory of the AI's mind in the user model: the intelligent system has a model of the user having a model of the intelligent system. We study a case where the system is a contextual bandit and the user model is a Markov decision process that plans based on a simpler model of the bandit. Inference in the model can be reduced to probabilistic inverse reinforcement learning, with the nested bandit model defining the transition dynamics, and is implemented using probabilistic programming. Our results show that improved performance is achieved if users can form accurate mental models that the system can capture, implying predictability of the interactive intelligent system is important not only for the user experience but also for the design of the system's statistical models.