Bidirectional interaction between power grid and buildings is a key characteristic of smart grids. Achieving a win-win situation for a grid and buildings with such interactions remains a challenge. Game theory is a powerful tool for using strategic analysis to identify the best interactions between multiple players. Stackelberg game can effectively reflect the core status of grid and the auxiliary position of buildings in this interaction (particularly in demand response programs), but no study used this game to establish such interactions while simultaneously considering the multiple requirements of grid and buildings, particularly for the commercial sector. In this study, therefore, basic and enhanced interaction strategies between a grid and buildings are developed using the Stackelberg game based on their identified Nash equilibria. The grid optimizes the price to maximize its net profit and reduce demand fluctuation, and individual building optimizes the hourly power demand to minimize electricity bill and effects of demand alternation from the baseline. In addition, the effects of building demand baseline uncertainty on the interaction are investigated and the enhanced robust interaction is proposed to deal with such uncertainty. Real site data of buildings on a campus in Hong Kong are used to validate the proposed interaction strategies. The results show that the proposed basic interaction increased net profit by 8% and reduced demand fluctuation by about 40% for the grid, with savings in electricity bills of 2.5-8.3% for the buildings. Moreover, the proposed robust interaction effectively relieved the negative effects caused by prediction uncertainty.