Device-to-Device communication allows a cellular user (relay node) to relay data between the base station (BS) and another cellular user (destination node). We address the problem of designing reverse auctions to assign a relay node to each destination node, when there are multiple potential relay nodes and multiple destination nodes, in the scenarios where the transmission powers of the relay nodes are: 1) fixed, 2) selected to achieve the data rates desired by destination nodes, and 3) selected so as to approximately maximize the BS's utility. We show that auctions based on the widely used Vickrey-Clarke-Groves (VCG) mechanism have several limitations in scenarios 1) and 2); also, in scenario 3), the VCG mechanism is not applicable. Hence, we propose novel reverse auctions for relay selection in each of the above three scenarios. We prove that all the proposed reverse auctions can be truthfully implemented as well as satisfy the individual rationality property. Using numerical computations, we show that in scenarios 1) and 2), our proposed auctions significantly outperform the auctions based on the VCG mechanism in terms of the data rates achieved by destination nodes, utility of the BS and/ or the interference cost incurred to the BS.

We consider a set of cellular users associated with a base station (BS) in a cellular network that employs Device-todevice (D2D) communication. A subset of the users request for some files from the BS. Now, some of the users can potentially act as relays and forward the requested files, or partitions of files, from the BS to some of the requesting users (destination nodes) over D2D links. However, this requires cooperation among the cellular users. Also, when cellular users cooperate with each other, the total amount of energy consumed in transferring the requested files from the BS to the destination nodes can usually be considerably reduced compared to the case when each user separately downloads the file it needs from the BS. In this paper, we seek conditions under which users have an incentive to cooperate with each other. To this end, we model the above scenario using the frameworks of cooperative game theory and stable partitions in coalitional games. We consider two different models for file transfer within a coalition: (i) Model A, in which the BS can split a file into multiple partitions and send these partitions to different relays, which multicast the partitions to the destination nodes of the coalition, and (ii) Model B, in which for each file, the BS sends the entire file to a single relay, which multicasts it to the destination nodes of the coalition. First, we explore the question of whether it is beneficial for all the cellular users to cooperate, i.e., whether the grand coalition is stable. For this we use the solution concept of core from cooperative game theory. We show that, in general, the above coalitional game under Model A may have an empty core, i.e., it may not be possible to stabilize the grand coalition. Next, we provide conditions under which 1) the core is always non-empty and 2) a Dc-stable partition always exists. Also, we show that under Model B, the problem of assigning relays to destination nodes so as to maximize the sum of utilities of all the users is NP-Complete. Finally, we show via numerical computations that a significant reduction in the energy expenditure of cellular users can be achieved via cooperation.