In order to suppress interference caused by the dense deployment of small cell base stations in an ultra-dense network (UDN) and improve system throughput, this paper investigates the power allocation strategy for a spectrum sharing UDN. Firstly, the noncooperative game was adopted to transform the non-convex system sum-rate maximization problem into several convex subproblems that maximize the utility function of each user. By designing a dynamic pricing, each Nash equilibrium point (NE) of the game was a stationary point of the original optimization problem. Secondly, an interference power constraint was applied to guarantee the quality-of-service (QoS) of the macrocell. Finally, under the game theory framework, an iterative global information-based power allocation algorithm was designed. The optimal transmit power of each user could be obtained by solving KKT condition during each iteration, and the proposed iterative algorithm was proved to be convergent to the NE of the game model. In addition, in order to reduce the signaling overhead and improve the resource utilization, a power allocation algorithm based on local information was also proposed. Simulation results show that the proposed global information-based power allocation algorithm achieved a better transmission performance than benchmark methods and the proposed local information-based power allocation algorithm effectively reduced signaling overhead while guaranteed good transmission performance.