While current Bitcoin literature mainly focuses on miner behaviors, little has been done to analyze user participation. Because Bitcoins users do not benefit from any incentive, their participation in the system is conditional upon system ability to provide a transactional service at a reasonable cost and acceptable quality. A recent observed trend on a growing number of unconfirmed transactions seems, however, to substantiate that Bitcoin is facing service degradation. The objective of this paper is to shed some light on user participation in Bitcoin against a notion of system fairness, through a utility-based approach. We first introduce fairness to quantify the satisfaction degree of participants (both users and miners) with respect to their justified expectations over time. We then characterize user strategies, deriving the necessary condition for fairness, and we show Bitcoin limitations in delivering it. The utility-based model allows to finally draw conclusions on possible improvements for fairness to promote user participation.