A self-avatar is known to have a potentially significant impact on the user's experience of the immersive content but it can also affect how users interact with each other in a shared virtual environment (SVE). We implemented an SVE for a consumer virtual reality system where each user's body could be represented by a jointed self-avatar that was dynamically controlled by head and hand controllers. We investigated the impact of a self-avatar on collaborative outcomes such as completion time and trust formation during competitive and cooperative tasks. We used two different embodiment levels: no self-avatar and self-avatar, and compared these to an in-person face to face version of the tasks. We found that participants could finish the task more quickly when they cooperated than when they competed, for both the self-avatar condition and the face to face condition, but not for the no self-avatar condition. In terms of trust formation, both the self-avatar condition and the face to face condition led to higher scores than the no self-avatar condition; however, collaboration style had no significant effect on trust built between partners. The results are further evidence of the importance of a self-avatar representation in immersive virtual reality.