Government investment in public health management can elicit strong responses from individuals within communities. These responses can reduce and even reverse the expected benefits of the policies. Therefore, projections of individual responses to policy can be important ingredients into policy design. Yet our foresight of individual responses to public health investment remains limited. This paper formulates a population game to explore how individual investment through behavior and government investment through taxation impact the health commons. We model the problem of infectious disease management through reductions in transmission risk for a disease that does not elicit immunity in a population without demographic structure. We identify three common modes of government and individual investments and describe how each mode relates to policy responses and health outcomes. We also provide general bounds on the magnitude of practical investment by individuals. The methods we present can be extended to address specific policy problems where public responses are expected to impose key feedbacks. Work done in collaboration with Darla Lindburg, Rachel A. Smith, and Timothy C. Reluga.