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Two critical issues in wireless sensor networks are cooperation of nodes and the limited availability of energy within network nodes. A widely employed energy-saving technique is to place nodes in sleep mode, corresponding to low-power consumption as well as to reduced operational capabilities. This causes a node may try to maximize the benefits it gets from the network without participating to its services (e.g. without forwarding packets of other nodes). To conquer with this problem, node cooperation schemes have been investigated in the literature. Therefore, it is crucial to find the optimal trade-off between the amount of cooperation and the amount of energy saving. In this work, we develop an analytical model of a sensor network which not only stimulates nodes to cooperation but also tries to satisfy energy consumption. In our scheme, nodes may enter a sleep mode while active nodes in a relay zone (Vakil and Liang, 2006) are allowed to cooperate with the source. We use this model to investigate the system performance in terms of node cooperation, energy consumption, and network capacity. Furthermore, the proposed model enables us to investigate the trade-off existing between these performance metrics. Numerical results show that the proposed scheme is successful in increasing node cooperation while energy consumption is satisfied.