Public policies that supply public goods, especially those involve collaboration by limiting individual liberty, always give rise to controversies over governance legitimacy. Multi-Agent Reinforcement Learning (MARL) methods are appropriate for supporting the legitimacy of the public policies that supply public goods at the cost of individual interests. Among these policies, the inter-regional collaborative pandemic control is a prominent example, which has become much more important for an increasingly inter-connected world facing a global pandemic like COVID-19. Different patterns of collaborative strategies have been observed among different systems of regions, yet it lacks an analytical process to reason for the legitimacy of those strategies. In this paper, we use the inter-regional collaboration for pandemic control as an example to demonstrate the necessity of MARL in reasoning, and thereby legitimizing policies enforcing such inter-regional collaboration. Experimental results in an exemplary environment show that our MARL approach is able to demonstrate the effectiveness and necessity of restrictions on individual liberty for collaborative supply of public goods. Different optimal policies are learned by our MARL agents under different collaboration levels, which change in an interpretable pattern of collaboration that helps to balance the losses suffered by regions of different types, and consequently promotes the overall welfare. Meanwhile, policies learned with higher collaboration levels yield higher global rewards, which illustrates the benefit of, and thus provides a novel justification for the legitimacy of, promoting inter-regional collaboration. Therefore, our method shows the capability of MARL in computationally modeling and supporting the theory of calculus of consent, developed by Nobel Prize winner J. M. Buchanan.