abstract: This dissertation discusses the Cournot competition and competitions in the exploitation of common pool resources and its extension to the tragedy of the commons. I address these models by using potential games and inquire how these models reflect the real competitions for provisions of environmental resources. The Cournot models are dependent upon how many firms there are so that the resultant Cournot-Nash equilibrium is dependent upon the number of firms in oligopoly. But many studies do not take into account how the resultant Cournot-Nash equilibrium is sensitive to the change of the number of firms. Potential games can find out the outcome when the number of firms changes in addition to providing the "traditional" Cournot-Nash equilibrium when the number of firms is fixed. Hence, I use potential games to fill the gaps that exist in the studies of competitions in oligopoly and common pool resources and extend our knowledge in these topics. In specific, one of the rational conclusions from the Cournot model is that a firm's best policy is to split into separate firms. In real life, we usually witness the other way around; i.e., several firms attempt to merge and enjoy the monopoly profit by restricting the amount of output and raising the price. I aim to solve this conundrum by using potential games. I also clarify, within the Cournot competition model, how regulatory intervention in the management of environmental pollution externalities affects the equilibrium number of polluters. In addition, the tragedy of the commons is the term widely used to describe the overexploitation of open-access common-pool resources. Open-access encourages potential resource users to continue to enter the resource up to the point where rents are exhausted. The resulting level of resource use is higher than is socially optimal, and in extreme cases can lead to the collapse of the resource and the communities that may depend on it. In this paper I use the concept of potential games to evaluate the relation between the cost of resource use and the equilibrium number of resource users in open access regimes. I find that costs of access and costs of production are sufficient to determine the equilibrium number of resource users, and that there is in fact a continuum between Cournot competition and the tragedy of the commons. I note that the various common pool resource management regimes identified in the empirical literature are associated with particular cost structures, and hence that this may be the mechanism that determines the number of resource users accessing the resource. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics for the Life and Social Sciences 2017