Collaboration is an essential aspect of human interaction. Despite being mutually beneficial to everyone involved, it often fails due to behaviour differences as individuals process information, form opinions, and interact with each other, especially when their task contains uncertainty. Thus, to understand collaboration on noisy problems effectively, it is necessary to consider the psychology of the individuals involved. We propose an agent-based model of collaboration that incorporates human psychology. We abstract the shared goal as a shared optimisation task, and model personality differences as strategies for moving within, interpreting and sharing information about the solution space. Although used to explore a specific hypothesis here, the model is psychology theoryagnostic and problem-independent and can also be used to investigate other tasks and different psychology theories.