The peak power of the manufacturing systems can increase electricity costs and reduce the use of renewable energy suppliers. The power of the machining processes depends on the processing time of the operations. Then, the allocation of the power to the machines of a manufacturing system controls the processing time of the manufacturing operations. An efficient allocation model can reduce the peak power, keeping the throughput performance level. This paper proposes a game theory to allocate the power to the machines including the dependence of the processing time from the power allocated. The game model uses the Gale-Shapley algorithm that forms couples of under and overloaded machines. Then, each couple exchanges the power from the underloaded to overloaded machines. The model considers the global workload and the jobs in queue for each machine. A simulation model tests the proposed method compared to a benchmark where each machine works with fixed power. The simulation results show how the model can improve the performance of the manufacturing system in several conditions tested. In particular, the main benefits can be obtained when the manufacturing system has high or medium utilization or the uncertainty affects the processing time.