The MQTT protocol has emerged over the past decade as a key protocol for a number of low power and lightweight communication scenarios including machine-to-machine and the Internet of Things. In this paper we develop a utility-based reputation model for MQTT, where we can assign a reputation score to participants in a network based on monitoring their behaviour. We mathematically define the reputation model using utility functions on participants based on the expected and perceived behaviour of MQTT clients and servers. We define an architecture for this model, and discuss how this architecture can be implemented using existing MQTT open source tools, and we demonstrate how experimental results obtained from simulating the architecture compare with the expected outcome of the theoretical reputation model.