In this paper, we investigate an auction based energy efficient link selection scheme in buffer-aided relay networks. The problem of link selection and power allocation is formulated as a Constrained Markov Decision Process (CMDP) problem, which is decomposed into two local CMDP problems at the relay node and the source node through auction method. The optimal link selection solution is determined by minimizing the power expenditure with respect to the instantaneous channel state information (CSI) and queue state information (QSI) in each time-slot. Stochastic approximation and the value function approximation approaches are employed to solve the local CMDP problems. Simulations demonstrate the theoretical solutions.