Algorithmic fairness is an essential requirement as AI becomes integrated in society. In the case of social applications where AI distributes resources, algorithms often must make decisions that will benefit a subset of users, sometimes repeatedly or exclusively, while attempting to maximize specific outcomes. How should we design such systems to serve users more fairly? This paper explores this question in the case where a group of users works toward a shared goal in a social exergame called Step Heroes. We identify adverse outcomes in traditional multi-armed bandits (MABs) and formalize the Greedy Bandit Problem. We then propose a solution based on a new type of fairness-aware multi-armed bandit, Shapley Bandits. It uses the Shapley Value for increasing overall player participation and intervention adherence rather than the maximization of total group output, which is traditionally achieved by favoring only high-performing participants. We evaluate our approach via a user study (n=46). Our results indicate that our Shapley Bandits effectively mediates the Greedy Bandit Problem and achieves better user retention and motivation across the participants.