We investigate the power allocation problem in interfering wireless networks. In the network, there are multiple sources with each transmitting to multiple destinations. By proposing a game, we are able to allocate power for each destination in a distributed way. Due to the possibility that the feasible set can be empty, our game can terminate the power allocation process upon detecting any infeasibility. We show that our game allocates power in a way such that the total transmit power is minimized. In general, the game works for interfering networks with arbitrary interference cancellation for the transmissions from the same source. As examples, we consider two schemes, namely interference transmission and cooperative broadcasting interference transmission. For converging cases, the schemes require within 60 iterations for convergence for over 90% of realizations. For cases without feasible solutions, the schemes require within 6 iterations for detecting the infeasibility for over 90% of realizations.