Network coding is a promising technique to improve the throughput and robustness of wireless ad hoc networks. However, the packet-mixing nature of network coding also renders it more prone to pollution attacks. Most existing schemes to combat pollution attacks did not consider the defender's resource limit, nor the trade-off between defensive performance and other metrics such as delay and resource consumption. The authors investigate how to achieve such a trade-off optimally by proposing a two-player strategic game model between the attack and the defender. In this model, the utilities of both players are well defined, and thus the defender can obtain its best strategy by maximising its utility. To do so, a graph-based simulated annealing algorithm is proposed to derive the utility-maximising strategy. Finally, they conduct extensive experiments to evaluate their scheme from different aspects. The results show that their scheme can achieve better utility than existing schemes, and is more computationally efficient in the meanwhile. Moreover, their scheme can obtain a sub-optimal solution within a small number of iterations, which implies that it can be implemented in the short-session communication scenario where it is required to find a sufficiently good solution within a short time.