Based on Game Theory and Multi-objective optimization problems (MOP), Game Optimization Theory (GOT) is discussed in this paper. Optimization Stability Analysis (OSA), Distance Entropy Multi-Objective Particle Swarm Optimization (DEMPSO) and Fuzzy Multi-weights Decision-making Method (FMW) are proposed as well. Game Optimization Theory, which is a comprehensive system, could not only handle multi-objective optimization problems effectively, but also could offset the disadvantages of traditional optimization theories, such as lack of framework and the insufficient consideration of relevant elements. In this paper GOT is used for the first time in solving the distribution systems planning (DSP) issue by implementing distributed generation. The proposed model integrates costs, losses, and voltage index to achieve optimal size and site of distributed generation. The model allows minimizing total system costs, system power losses and maximizing voltage improvement. A detailed DSP example is used for verifying the effectiveness and reasonableness of GOT in this context.