Communication gains from relaying can be acquired even in the absence of altruistic or dedicated relays. To accommodate this, spectrum leasing for cooperation paradigm prescribes that the potential relaying node is rewarded for its relaying role with a fraction of source's bandwidth. Recently, a two-hop spectrum leasing scheme was proposed that enables the source to employ the relay only to an extent it finds beneficial, preserving the remaining bandwidth for its direct transmission, if necessary. Such a solution adds flexibility that can be particularly useful for implementation in networks involving more than two hops. In this paper, we extend this setup to include the relay selection problem in a two-hop network scenario with multiple potential relays. Since the potential relays are selfish nodes, their competitive attitude for accessing the spectrum needs to be taken into account. In addition to Stackelberg game framework used in the original setting with one relay, auction theory is applied to model the relay selection process. Analysis and numerical results are provided, demonstrating that the source-destination pair can achieve significant benefits emanating from the competitive nature of the relays.