A hybrid active-passive wireless sensor network (HWSN) is a cost-effective and energy-efficient way for localization systems. The active sensor nodes, which are targets, can locate themselves by sending wireless power signals to power up the passive sensors, or via cooperative localization among targets. The common used power allocation approaches e.g., semi-definite programming (SDP), are aiming to minimize the overall localization error with energy constraints. However, the global optimum may lead to issues such as decreased individual performance and unbalanced network resources. To address the above challenges, we propose a game theory power allocation framework for the cooperative localization of HWSNs in this paper. We present the Fisher information matrix (FIM) and the corresponding squared position error bound (SPEB) for two types of HWSNs, which are the general cooperation network and tree topology network. For the general cooperation network, we derive the closed-form solution of optimal power allocation using the general bargaining equilibrium. In the tree topology network, we propose a Stackelberg equilibrium approach that effectively adapts the power allocation scheme based on the obtained hierarchical information structure. Extensive simulation results demonstrate that the proposed method outperforms semidefinite programming (SDP) and equal power allocation scheme (EQ) in position estimation error. Specifically, compared to other schemes, our proposed scheme has improved the positioning accuracy by 75% in the general cooperation network and by 70% in the tree topology network.