In this paper, a non-cooperative game theoretic power allocation (NGTPA) scheme is proposed for coexisting multistatic radar and wireless communication systems. Due to the fact that each radar in the system is selfish-interested to maximize its own utility, we utilize the non-cooperative game theory to tackle the power allocation problem. The main objective of the multistatic radar is to minimize the power consumption of each radar by optimizing the transmission power allocation, which are constrained by a predefined signal-to-interference-plus-noise ratio (SINR) requirement for target detection and a maximum acceptable interference power threshold for communication system. First, taking into consideration the target detection performance and received interference power at the communication receiver, a novel utility function is defined and adopted as the optimization criterion for the NGTPA strategy. Then, the existence and uniqueness of the Nash equilibrium (NE) point are analytically proved. Furthermore, an iterative power allocation algorithm is developed that converges quickly to the NE of the non-cooperative game model. Numerical simulations are provided to demonstrate the superior performance of the proposed NGTPA algorithm.