Energy conservation is the key factor driving the trend toward green next-generation wireless networks. Existing studies have shown that cooperative communications can significantly reduce energy consumption. Most of these studies simplistically assume that all of the nodes in the network will cooperatively transmit. However, in practice, nodes may not always be altruistic and reject collaboration. Accordingly, this study proposes a reputation auction framework to provide indirect reciprocity for stimulating node cooperation in green wireless networks which also adapts to various network dynamics. Two sealed-bid auction schemes are presented to efficiently and fairly allocate node reputation for single and multiple relay scenarios resulting in energy savings arising from application of the considered indirect reciprocity model. The simulation results show that the proposed reputation auction framework can achieve higher energy efficiency compared to non-cooperative schemes and only slightly increases signaling overhead.