Glaucoma is the leading cause of irreversible but preventable blindness worldwide, and visual field testing is an important tool for its diagnosis and monitoring. Testing using standard visual field thresholding procedures is time-consuming, and prolonged test duration leads to patient fatigue and decreased test reliability. Different visual field testing algorithms have been developed to shorten testing time while maintaining accuracy. However, the performance of these algorithms depends heavily on prior knowledge and manually crafted rules that determine the intensity of each light stimulus as well as the termination criteria, which is suboptimal. We leverage deep reinforcement learning to find improved decision strategies for visual field testing. In our proposed algorithms, multiple intelligent agents are employed to interact with the patient in an extensive-form game fashion, with each agent controlling the test on one of the testing locations in the patient's visual field. Through training, each agent learns an optimized policy that determines the intensities of light stimuli and the termination criteria, which minimizes the error in sensitivity estimation and test duration at the same time. In simulation experiments, we compare the performance of our algorithms against baseline visual field testing algorithms and show that our algorithms achieve a better trade-off between estimation accuracy and test duration. By retaining testing accuracy with reduced test duration, our algorithms improve test reliability, clinic efficiency, and patient satisfaction, and translationally affect clinical outcomes.