Free riding at group coursework is a common practice in a university setting. It can be analysed from a game- theoretical perspective as a variant of the prisoner dilemma, with the difference that encounters do not happen between two individuals, but a group of them. This paper proposes a simple model that characterised the group coursework problem and deduces the behaviour of the system by three different methods, namely an analytical integration, a numerical integration, and an agent-based model. By an analysis of the results, the system shows a sigmoid-like behaviour ending up in one of two polarized modes: everybody cooperates or everybody defects, depending on the model parameters. Finally, a more complex model with a network topology is proposed and simulated, showing possible equilibriums at mixed states in the population.