Numerous safety-related applications have rigid requirements for the threshold of latency limitation of message transmissions to enhance safety and traffic efficiency of vehicles on the road in vehicular ad-hoc networks (VANETs). Consequently, a medium access control (MAC) protocol for reliable and fast transmission of safety messages should focus on the maximum transmission delay. Herein, we refer to the concept of packet value and integrate it with the latency of different messages determined by the waiting interval of packets in a queue. Subsequently, we propose a reciprocal revenue function, i.e., the transmission probability of the participants, by considering both its own benefit and the other nodes’ revenue. Additionally, an inter-vehicle cross-layer cooperative game model based on the local optimal utility of participants is constructed. We then theoretically prove the existence of an equilibrium using the partially observable Markov decision process (POMDP), and provide a specific approach for obtaining the channel access probability of a vehicle by using deep reinforcement learning. Finally, the analysis and simulation results in saturated and non-saturated data traffic conditions are presented to evaluate the performance of Reciprocal Partially Observable MAC Protocol (RPO-MAC) proposed in this paper and compare it with the IEEE 802.11p standard protocol. These comparisons demonstrate the advantages of our proposed reciprocal revenue game method in the case of channel network congestion, especially in terms of delay. It is shown that the RPO-MAC protocol can provide a strong support to delay-sensitive safety related applications.