Cooperative intelligence (CI) is expected to become an integral element in next-generation networks because it can aggregate the capabilities and intelligence of multiple devices. Multi-agent reinforcement learning (MARL) is a popular approach for achieving CI in communication problems by enabling effective collaboration among agents to address sequential problems. However, ensuring privacy protection for MARL is a challenging task because of the presence of heterogeneous agents that learn interdependently via sharing information. Implementing privacy protection techniques such as data encryption and federated learning to MARL introduces the notable overheads (e.g., computation and bandwidth). To overcome these challenges, we propose PP-MARL, an efficient privacy-preserving learning scheme for MARL. PP-MARL leverages homomorphic encryption (HE) and differential privacy (DP) to protect privacy, while introducing split learning to decrease overheads via reducing the volume of shared messages, and then improve efficiency. We apply and evaluate PP-MARL in two communication-related use cases. Simulation results reveal that PP-MARL can achieve efficient and reliable collaboration with 1.1-6 times better privacy protection and lower overheads (e.g., 84-91% reduction in bandwidth) than state-of-the-art approaches.