The collaborative aspect of games has been shown to potentially increase player performance and engagement over time. However, collaborating players need to perform well for the team as a whole to benefit and thus teams often end up performing no better than a strong player would have performed individually. Personalisation offers a means for improving overall performance and engagement, but in collaborative games, personalisation is seldom implemented, and when it is, it is overwhelmingly passive such that the player is not guided to goal states and the effectiveness of the personalisation is not evaluated and adapted accordingly. In this paper, we propose and apply the use of reflective agents to personalisation ('reflective personalisation') in collaborative gaming for individual players within collaborative teams via a combination of individual player and team profiling in order to improve player and thus team performance and engagement. The reflective agents self-evaluate, dynamically adapting their personalisation techniques to most effectively guide players towards specific goal states, match players and form teams. We incorporate this agent-based approach within a microservices architecture, which itself is a set of collaborating services, to facilitate a scalable and portable approach that enables both player and team profiles to persist across multiple games. An experiment involving 90 players over a two-month period was used to comparatively assess three versions of a collaborative game that implemented reflective, guided, and passive personalisation for individual players within teams. Our results suggest that the proposed reflective personalisation approach improves team player performance and engagement within collaborative games over guided or passive personalisation approaches, but that it is especially effective for improving engagement.