Aiming at the problem of the two-way interaction between the smart grid and the demand side, the benefits of the grid and the demand side are difficult to take into account at the same time, this paper proposes a strategy for interactive management of the smart grid and the demand side based on game theory. This strategy uses the Stackelberg game to keep the confrontation strategy between the grid and the demand side always in a Nash equilibrium state, thereby ensuring that the interests of both parties are maximized. In addition, this paper also studies the impact of demand baseline forecasting on interactive strategies, and proposes enhanced interactive strategies to deal with this uncertainty. Finally, this paper takes the Hong Kong Polytechnic University as an example for simulation analysis to verify the effectiveness of the strategy. The results show that the proposed strategy can increase the net profit of the power grid by 8%, reduce the fluctuation of demand by about 40%, and save electricity costs by 2.5-8.3% on the demand side. In addition, the enhanced interaction strategy can also effectively mitigate the negative impact caused by inaccurate baseline demand forecasting.