Wireless power charging enables portable devices to be permanently unplugged. Due to its low transmission power and low transmission efficiency, it requires much longer time slot to charge users compared with that for data transmission in wireless communication networks. Besides, each user's demand urgency needs to be taken into consideration for power allocation. Therefore, new algorithms are essential for wireless power allocation in multi-user wireless charging networks. In this paper, this problem is formulated as a static noncooperative game. It is shown that there exists a unique Nash equilibrium, which is the static state of the wireless power charging network. A distributed power allocation algorithm is proposed to compute the Nash equilibrium of the game. The main result of the paper consists of rigorous analysis of the distributed algorithm for power allocation. The algorithm is shown to converge to Nash equilibrium of the game with exponentially convergence rate for arbitrary initial value with synchronous scheduling. Moreover, the distributed algorithm is also convergence guaranteed with asynchronous scheduling under communication delay and packet drops. Numerical simulations prove the correctness of the analysis and demonstrate the fast convergence of the algorithm and the robustness to synchronous scheduling.