Multi-tenancy is a key pillar of cloud services. It allows different tenants to share computing resources transparently and, at the same time, guarantees substantial cost savings for the providers. However, from a user perspective, one of the major drawbacks of multi-tenancy is lack of configurability. Depending on the isolation degree, the same service instance and even the same service configuration may be shared among multiple tenants (i.e. shared multi-tenant service). Moreover tenants usually have different -and in most of the cases -conflicting configuration preferences. To overcome this limitation, this paper introduces a novel approach to support user-centric adaptation in shared multi-tenant services. The adaptation objective aims to maximise tenants' satisfaction, even when tenants and their preferences change during the service life-time. This paper describes how to engineer the activities of the MAPE loop to support user-centric adaptation, and focuses on the analysis of tenants' preferences. In particular, we use a game theoretic analysis to identify a service configuration that maximises tenants' preferences satisfaction. We illustrate and motivate our approach by utilising a multi-tenant desktop scenario. Obtained experimental results demonstrate the feasibility of the proposed analysis.