Scarcity of health care resources could result in the unavoidable consequence of rationing. For example, ventilators are often limited in supply, especially during public health emergencies or in resource-constrained health care settings, such as amid the pandemic of COVID-19. Currently, there is no universally accepted standard for health care resource allocation protocols, resulting in different governments prioritizing patients based on various criteria and heuristic-based protocols. In this study, we investigate the use of reinforcement learning for critical care resource allocation policy optimization to fairly and effectively ration resources. We propose a transformer-based deep Q-network to integrate the disease progression of individual patients and the interaction effects among patients during the critical care resource allocation. We aim to improve both fairness of allocation and overall patient outcomes. Our experiments demonstrate that our method significantly reduces excess deaths and achieves a more equitable distribution under different levels of ventilator shortage, when compared to existing severity-based and comorbidity-based methods in use by different governments.