We applied evolutionary game theory to extend a resource constrained security game model for confidentiality attacks in an Advanced Metering Infrastructure (AMI), which is a component of IoT-enabled Smart Grids. The AMI is modelled as a tree structure where each node aggregates the information of its children before encrypting it and passing it on to its parent. As a part of the model, we developed a discretization scheme for solving the replicator equations. The aim of this work is to explore the space of possible behaviours of attackers and to develop a framework where the AMI nodes adaptively select the most profitable strategies. Using this model, we simulated the evolution of a population of attackers and defenders on various cases resembling the real life implementation of AMI. We discuss in depth how to enhance security in AMI using evolutionary game theory either by a priori analysis or as a tool to run dynamic and adaptive infrastructure defence.