Feedback mechanism has been widely used in wireless communication such as channel equalization and resource allocation. In recent years, deep learning (DL) has made great progress in the field of wireless communication. There is now some work that attempts to introduce plain feedback mechanisms into DL algorithm to solve wireless communication problems. However, the improvement of plain feedback DL methods is limited in complex situations due to those methods lack sufficient learning ability on feedback information. In this paper, we propose a Multi-Agent Feedback Enabled Neural Network (MAFENN) equalizer, which consists of a specific learnable feedback agent and two feed-forward agents. Three fully cooperative intelligent agents help the system improve the ability to remove wireless inter-symbol interference (ISI) in receiving ends. We further formulate it into a three-player Stackelberg Game, which helps us to optimize and train this model more efficiently. To verify the feasibility of our proposed MAFENN system and the Stackelberg Game optimization, we conduct a series of experiments to compare the symbol error rate (SER) performance of the MAFENN equalizer and the other methods which utilizes quadrature phase-shift keying (QPSK) modulation scheme. Our performance outperforms that of the other equalizers at different signal-to-noise ratio (SNR) settings for both linear and nonlinear channels.