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Device-to-device (D2D) communications are recognized as a key enabler of future cellular networks, which will help to drive improvements in spectral efficiency and assist with the offload of network traffic. Relay-assisted D2D communications will be essential when there is an extended distance between the source and the destination or when the transmit power is constrained below a certain level. Although a number of works on relay-assisted D2D communications have been presented in the literature, most of those assume that relay nodes cooperate unequivocally. In reality, this cannot be assumed, since there is little incentive to cooperate without a guarantee of future reciprocal behavior. To incorporate the social behavior of D2D nodes, we consider the decision to relay using the donation game based on social comparison, characterize the probability of cooperation in an evolutionary context and then evaluate …