In this paper, we consider a two-hop network with a source node (SN) and a relay node (RN) who want to communicate data to a destination node (DN). The SN cannot be directly connected to the DN, but rather is connected only via the RN. The RN does not have an external source of energy, and thus needs to harvest energy from the SN to communicate, while the SN has an external source of energy and can harvest energy straight from it. Thus, a dilemma for the SN arises: how much to share harvested energy with the RN to make it relay the SN’s data to the DN. Fair performing of their communication tasks is considered as an incentive for the SN and the RN to cooperate. The optimal α fair schedule is found for each α. It is shown that an altruistic strategy for one of the nodes comes in as a part of the cooperative solution (corresponding α= 0 ), while the maxmin strategy (corresponding α tending to infinity) is proved to be egalitarian. Using Nash bargaining over the obtained continuum of fair solutions, we design a trade-off strategy.