Device-to-device (D2D) communication has recently attracted much research attention because of its potential to increase the capacity of cellular networks. Most existing works aim to maximise the overall system throughput (systemcentric), which ignores the actual traffic demands of D2D users. In this study, the authors consider user-centric relay assisted D2D communications where D2D users have different evaluations for the significance of every unit of increased data rate. By considering the traffic demands of D2D users, the authors propose a Vickrey-Clarke-Groves auction based relay allocation mechanism (ARM) in which every D2D user submits a bid to the basestation (BS). The submitted bids indicate D2D users' valuation on every unit of the increased data rate. The BS then allocates relays to D2D users by maximising the social welfare of D2D users while maintaining a predefined data rate requirement for cellular users. A payment scheme to charge D2D users for using relays is designed, and the authors show that the auction is truthful. The authors also extend the results to a general case and provide a general ARM accordingly. Extensive simulation results are provided to demonstrate the performance of the proposed mechanisms.