Device-to-device (D2D) communications are recognizedudas a key enabler of future cellular networks which willudhelp to drive improvements in spectral efficiency and assistudwith the offload of network traffic. Among the transmissionudmodes of D2D communications are single-hop and relay assistedudmulti-hop transmission. Relay-assisted D2D communications willudbe essential when there is an extended distance between theudsource and destination or when the transmit power of D2D userudequipments (UEs) is constrained below a certain level. Althoughuda number of works on relay-assisted D2D communications haveudbeen presented in the literature, most of those assume that relayudnodes cooperate unequivocally. In reality, this cannot be assumedudsince there is little incentive to cooperate without a guarantee ofudfuture reciprocal behavior. Cooperation is a social behavior thatuddepends on various factors, such as peer comparison, incentives,udthe cost to the donor and the benefit to the recipient. Toudincorporate the social behavior of D2D relay nodes, we considerudthe decision to relay using the donation game based on socialudcomparison and characterize the probability of cooperation inudan evolutionary context. We then apply this within a stochasticudgeometric framework to evaluate the outage probability andudtransmission capacity of relay assisted D2D communications.udThrough numerical evaluations, we investigate the performanceudgap between the ideal case of 100% cooperation and practicaludscenarios with a lower cooperation probability. It shows thatudpractical scenarios achieve lower transmission capacity andudhigher outage probability than idealistic network views whichudassume full cooperation. After a sufficient number of generations,udhowever, the cooperation probability follows the natural rules ofudevolution and the transmission performance of practical scenariosudapproach that of the full cooperation case, indicating that all D2Dudrelay nodes adopt the same dominant cooperative strategy basedudon social comparison, without the need for enforcement by anudexternal authority.
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