The evolution of cooperation in continuous dilemmas via multi-agent reinforcement learning

Abstract

The evolution of cooperation aims to investigate how to increase the proportion of cooperating participants in a system. It has been studied in a broad range of domains from biology and social science to multi-agent systems and control systems. However, the current research shares a common limitation in that each participant can only opt for cooperation or defection. In the real-world, however, whether to cooperate or defect may not be a strict option; rather, it might be measured in multiple levels. To address this issue, we first propose a novel continuous dilemma in the federated learning setting called the malicious client’s dilemma, where malicious clients can quantify the poisonous updates that will be sent to the server. A multi-agent reinforcement learning-based method that involves a deep prediction network and a deep generation network is then developed to deal with the continuous dilemma. Taking each participant in turn, the deep prediction network predicts the behavior of the other participants in the current round based on their previous behavior. Then, based on the prediction, the deep generation network generates an action for the participant. We theoretically prove that, by combining the two networks, both the learning stationarity and convergence can be guaranteed. A comprehensive set of experiments comparing our method with two other state-of-the-art methods also based on reinforcement learning demonstrates the superior performance of our method in both the proposed dilemma and two other prevalent dilemmas. Our method achieves better results in promoting cooperation and obtaining higher rewards through its unique ability to predict other agents’ behavior and generate optimal strategies based on these predictions, while existing methods rely solely on historical behaviors or reputation mechanisms.