Abstract: ‍ ‍In recent years， deep learning （DL） has been increasingly used in communication scenarios， such as for digital predistortion （DPD） of radio frequency （RF） transmitters. However， the nonlinear distortion and memory effects of power amplifiers （PAs） are non-negligible obstacles for traditional DL algorithms. Therefore， in this paper， we proposed a Multi-Agent Feedback Enabled Neural Network for Digital Predistortion （MAFENN-DPD）， which employed a feedback agent with high error correction capability. In addition， we employed information bottleneck theory to guide the network hyperparameter design and facilitated network training acceleration via Stackelberg game theory. We performed a series of experiments to validate our proposed MAFENN-DPD. The adjacent channel power ratio （ACPR） was improved by about 5 dB compared to the DPD implemented using a typical feedforward network. At the same time， without extensive prior knowledge of the communication process， the MAFENN-DPD achieved a nearly equivalent ACPR performance to the DPD modeled by memory polynomials. Therefore， we can assume that MAFENN， a novel network structure， has the ability to solve the nonlinearity problem and memory effects of PA and has the potential to be applied in other communication scenarios.