As wireless services and applications become more sophisticated and require faster and higher-capacity networks, there is a need for an efficient management of the execution of increasingly complex tasks based on the requirements of each application. In this regard, fog computing enables the integration of virtualized servers into networks and brings cloud services closer to end devices. In contrast to the cloud server, the computing capacity of fog nodes is limited and thus a single fog node might not be capable of computing-intensive tasks. In this context, task offloading can be particularly useful at the fog nodes by selecting the suitable nodes and proper resource management while guaranteeing the Quality-of-Service (QoS) requirements of the users. This paper studies the design of a joint task offloading and resource allocation control for heterogeneous service tasks in multi-fog nodes systems. This problem is formulated as a partially observable stochastic game, in which each fog node cooperates to maximize the aggregated local rewards while the nodes only have access to local observations. To deal with partial observability, we apply a deep recurrent Q-network (DRQN) approach to approximate the optimal value functions. The solution is then compared to a deep Q-network (DQN) and deep convolutional Q-network (DCQN) approach to evaluate the performance of different neural networks. Moreover, to guarantee the convergence and accuracy of the neural network, an adjusted exploration-exploitation method is adopted. Provided numerical results show that the proposed algorithm can achieve a higher average success rate and lower average overflow than baseline methods.