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In Cognitive radio ad hoc networks (CRAHNs), the secondary users (SUs) or cognitive radio nodes (CRs) are always equipped with limited energy and have a high error probability of data transmission. To address this issue, we first describe the network utility under energy constraint as a max-min model, where the re-transmission strategy with network coding is employed. Additionally, the expression of retransmission probability is presented in terms of power and bit error rate (BER). Moreover, since the max-min model is non-convex in both objective and constraints, we use a normal-form game to find a near-optimal solution. The simulation results show that the proposed approach could achieve a higher network utility than the compared approaches.