This dissertation consists of three chapters; each models competition in natural gas markets. These models provide insight into interactions between changes in market conditions/policies and market players’ strategic behavior. In all three chapters, we apply our models to a natural gas trade network formed by using BP’s Statistical Review of World Energy 2010 major trade flows. In the first chapter, we develop a model for the world natural gas market where buyers and sellers are connected by a trading network. Each natural gas producer is a Cournot player with a fixed supply capacity. Each of them is also connected to a unique set of importing markets. We show that this constrained noncooperative Cournot game is a potential game and its potential function has a unique maximizer. In the scenario analysis, we find that any exogenous change affecting Europe also has an effect in the Asia Pacific. The reason is that two big producers, Russia and the Middle East, are connected to both markets. We also find that a collusive agreement between Russia and the Middle East leads them to specialize in supply to markets based on their marginal costs of exporting natural gas. The second chapter is devoted to analyzing the impacts of North American shale gas on the world natural gas market. To better represent the North American natural gas market, this chapter also allows for perfect competition in that market. We find that North America exports natural gas when its supply curve is highly elastic and hence the domestic price impact of its exports is very small. Even so, the price impacts on the importing markets are substantial. We also find that shale gas development in North America decreases dominant producers’ market power elsewhere in the world and hence decreases the incentive of any parties to form a natural gas cartel. In the third chapter, we relax the assumption of fixed supply capacities and allow for natural gas producers to invest in their supply capacities. We assume a two period model with no uncertainty and show that there is a unique Cournot-Nash equilibrium and the open-loop Cournot-Nash equilibrium and closed-loop Cournot-Nash equilibrium investments coincide.

The rapid growth of peer-to-peer (P2P) networks in the past few years has brought with it increases in transit cost to Internet Service Providers (ISPs), as peers exchange large amounts of traffic across ISP boundaries. This ISP oblivious behavior has resulted in misalignment of incentives between P2P networks|that seek to maximize user quality|and ISPs|that would seek to minimize costs. Can we design a P2P overlay that accounts for both ISP costs as well as quality of service, and attains a desired tradeoff between the two? We design a system, which we call MultiTrack, that consists of an overlay of multiple kinds of Trackers whose purpose it is to align these goals. We have mTrackers that form an overlay network among themselves, and split demand from users among different ISP domains while trying to minimize their individual costs (delay plus transit cost) in their ISP domain. We design the signals in this overlay of mTrackers in such a way that potentially competitive individual optimization goals are aligned across the mTrackers. The system could also have a tTracker that acts as a gateway into the system, and ensures that users who are from different ISP domains have a fair chance of being admitted into the system, while keeping costs in check. We prove analytically that our system is stable and achieves maximum utility with minimum cost. We validated our system design using Matlab simulations, and implemented the system on ns-2 in order to conduct more realistic experiments. We showed that our system significantly outperforms two types of systems, one in which user delay is the only control dimension (forwarding traffic without considering the transit prices) and a second system in which transit prices are the only control dimension (localized traffic only). Thus, we conclude that our system, that operates in two dimensions: (1) user delay and (2) transit prices, results in minimum cost and maximum utility for fixed capacity of the system.

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

This thesis presents frameworks for the optimal strategic production planning of petroleum refineries operating in competition in multiple markets. The game theoretic concept of the Cournot oligopoly is used as the basic competitive model, and the Nash equilibrium as the solution concept for the formulated problems, which are reformulated into potential games. Nonlinear programming potential game frameworks are developed for static and dynamic production planning problems, as well for mixed integer nonlinear expansion planning problems in which refiners have access to potential upgrades increasing their competitiveness. This latter model represents a novel problem in game theory as it contains both integer and continuous variables and thus must satisfy both discrete and continuous mathematical definitions of the Nash equilibrium. The concept of the mixed-integer game is introduced to explore this problem and the theoretical properties of the new class of games, for which conditions are identified defining when a class of two-player games will possess Nash equilibria in pure strategies, and conjectures offered regarding the properties of larger problems and the class as a whole. In all examples, petroleum refinery problems are solved to optimality (equilibrium) to illustrate the competitive utility of the mathematical frameworks. The primary benefit of such frameworks is the incorporation of the influence of market supply and demand on refinery profits, resulting in rational driving forces in the underlying production planning problems. These results are used to justify the development of frameworks for enterprise optimization as a means of decision making in competitive industries. / Thesis / Doctor of Philosophy (PhD) / This thesis presents a mathematical framework in which refinery production planning problems are solved to optimal solutions in competing scenarios. Concepts from game theory are used to formulate these competitive problems into mathematical programs under single objective functions which coordinate the interests of the competing refiners. Several different cases are considered presenting refinery planning problems as static and dynamic programs in which decisions are time independent or dependent, respectively. A theoretical development is also presented in the concept of the mixed integer game, a game theoretic problem containing both continuous and discrete valued variables and which must satisfy both continuous and discrete definitions of Nash equilibrium. This latter development is used to examine refinery problems in which individual refiners have access to numerous unit upgrades which can potentially improve performance. The results are used to justify a game theoretic approach to enterprise optimization.