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This paper presents a game theoretical solution to the difficult challenge of optimal pitch sequencing. We model the batter/pitcher matchup as a zero-sum game and determine the equilibrium strategy for both the pitcher and batter. We conclude that the Stackelberg equilibrium and our newly defined decision point equilibrium serve as effective pitch sequencing strategies.

California state officials have continued to warn and encourage preparedness for the growing threats of water scarcity. This puts pressure on water suppliers to develop technological and managerial solutions to alleviate the problems associated with scarcity. A recent popular management strategy for distributing water is encouraging water transfers. While there has been analyses on water transfers between large districts and agencies, little analysis has been completed for smaller scale trades, i.e. between individuals in the same water district. This analysis models an agricultural water district, based on the Berrenda Mesa Water District (BMWD). In the model, the growers in the district have the collective goal of profit maximization, and the district has the goal of maximizing revenue from agriculture. The district decides if either long term or short term transfers are allowed between growers, who themselves decide to either elect to save more water or trade more water. A game theory simulation model is used to determine the best cooperative management strategy (BCSC), which is defined as a strategy combination which is Pareto optimal and a Nash equilibrium, or Pareto optimal and there are no Nash equilibria. Ultimately, the strategy combination of the district allowing short term trades and the growers electing to sell more water is the BCSC in all tested water scarcity scenarios.

Power systems have evolved significantly during the last two decades with the advent of Distributed Energy Resources (DERs) like solar PV. Traditionally, large power plants were considered as the sole source of energy in the power systems. However, DERs connected to the transmission and the distribution systems are creating a paradigm shift from a centralized generation to a distributed one. Though the variable power output from these DERs poses challenges to the reliable operation of the grid, it also presents opportunities to design control and coordination approaches to improve system efficiency and operational reliability. Moreover, building new transmission lines to meet ever-increasing load demand is not always viable. Thus, the industry is leaning towards developing non-wires alternatives. Considering the existing limitations of the transmission system, line congestions, and logistic/economic constraints associated with its capacity expansion, leveraging DERs to supply distribution system loads is attractive and thus capturing the attention of researchers and the electric power industry. The primary objective of this dissertation is to develop a framework that enables DERs to supply local area load by co-simulating the power system and transactive system representations of the network. To realize this objective, a novel distributed optimization and game theory-based network representation is developed that optimally computes the power output of the Home Microgrids/DER aggregators. Moreover, the optimum operational schedules of the DERs within these Home Microgrids/DER aggregators are also computed. The novel electrical-transactive co-simulation ensures that the solution is optimum in the context of power systems i.e. power flow constraints are not violated while the payoffs are maximized for the Home Microgrids/DER aggregators. The transactive mechanism involves two-way iterative signaling. The signaling is modeled as an infinite strategy, multiplayer, non-cooperative game, and a novel theory is developed for the game model. The dissertation also introduces a novel concept of ranking the Home Microgrids/DER aggregators according to their historic performance, thus leading to fairness, higher participation, and transparency. Significant advantages offered by the framework include consumption of local generation, transmission upgrade deferral, mitigation of line congestions in peak periods, and reduced transmission systems losses. / Doctor of Philosophy / In past, electricity was primarily produced by the large fossil fuel-based and nuclear power plants, usually located farther away from the populated areas where the bulk of the electricity consumption occurs. The electricity from the power plants is carried by the transmission lines to the populated areas where it is distributed to end-users via a distribution network. However, during the last two decades, issues like global warming and depleting fossil fuels have led to the development and increased adoption of renewable energy resources like solar photovoltaics (PV), wind turbines, etc. These resources are commonly known as Distributed Energy Resources (DERs), and they are connected to both the transmission and the distribution systems. Initially, they were mainly used to supply the load within the facility in which they are installed. However, the electric load (demand) continues to grow while adding new fossil fuel-based plants and transmission lines are becoming logistically/economically challenging. Thus, researchers are working on developing techniques that can enable DERs to supply the loads in the distribution system to which they are connected. This dissertation develops a method to use DERs for load support in the distribution systems. Specifically, the buildings that house the DERs can use the energy generated by the DERs to supply the local load (building load), and once the total generation exceeds the load demand, the building can inject the power into the distribution system to support the local area load. The proposed framework considers the electric network constraints like limits of lines supplying the power and limits of the transformers. The proposed work also develops a new method to maximize the benefit (in terms of profit) for the DER owners. A ranking system is introduced for the DER owners that enhances the transparency and fairness of the process. The key benefits offered by the proposed work include reduced losses in the transmission system, more energy consumed closer to the point of generation, and avoidance of transmission line and large central generation additions.

No / Due to the attractive characteristics of high capacity, high-speed, wide coverage and low transmission power, Wireless Mesh Networks become the ideal choice for the next-generation wireless communication systems. However, the network congestion of WMNs deteriorates the quality of service provided to end users. Game theory optimization model is a novel modeling tool for the study of multiple entities and the interaction between them. On the other hand, cross-layer design is shown to be practical for optimizing the performance of network communications. Therefore, a combination of the game theory and cross-layer optimization, named cross-layer game optimization, is proposed to reduce network congestion in WMNs. In this paper, the network congestion control in the transport layer and multi-path flow assignment in the network layer of WMNs are investigated. The proposed cross-layer game optimization algorithm is then employed to enable source nodes to change their set of paths and adjust their congestion window according to the round-trip time to achieve a Nash equilibrium. Finally, evaluation results show that the proposed cross-layer game optimization scheme achieves high throughput with low transmission delay.

The problem of causal discovery is to learn the true causal relations among a system of random variables based on the available data. Learning the true causal structure of p variables can sometimes be difficult, but it is crucial in many fields of science, such as biology, sociology and artificial intelligence. Classically, it is assumed that the true causal relations are completely encoded via a directed acyclic graph (DAG), and there are numerous algorithms for estimating a DAG representative of a causal system from data. Assuming it is feasible, the most effective way of learning the true causal structure is through interventional experiments. Eberhardt et al. identified the sufficient and in the worst case necessary number of interventions needed to learn a DAG, and then studied this problem from a game theory perspective, providing an upper bound on the expected number of experiments needed to identify the causal DAG. Here, we consider more general causal models, the CStrees, which allow for the true causal relations to be context-specific. We extend the results of Eberhardt to the family of CStrees by finding the sufficient and in the worst case necessary number of experiments the Scientist must perform in order to discover the true CStree among p variables. We generalize the game theoretic approach presented in Eberhardt's paper, to the CStrees with a specified causal ordering. We also give a geometric description of context-specific hard interventions in CStrees, through a bijection between the stages of the CStree and the faces of a polytope. / Problemet med kausal upptäckt är att lära sig de verkliga orsakssambandet mellan ett system av slumpmässiga variabler baserat på tillgängliga data. Att lära sig den sanna kausala strukturen hos p variabler kan ibland vara svårt, men det är avgörande inom många vetenskapsområden, såsom biologi, sociologi och artificiell intelligens. Klassiskt antas det att de sanna orsakssambandet är helt kodade via en riktad acyklisk graf (DAG), och det finns många algoritmer för att uppskatta en DAG-representant för ett orsakssystem från data. Förutsatt att det är genomförbart är det mest effektiva sättet att lära sig den sanna kausala strukturen genom interventionella experiment. Eberhardt et al. identifierade det tillräckliga och i värsta fall nödvändiga antalet insatser som behövdes för att lära sig en DAG, och studerade sedan detta problem ur ett spelteoriperspektiv, vilket gav en övre gräns för det förväntade antalet experiment som behövs för att identifiera orsakssambandet DAG. Här anser vi att mer allmänna orsakssambandet, CStrees, gör det möjligt att vara kontextspecifik för de verkliga orsakssambandet. Vi utvidgar resultaten av Eberhardt till familjen CStrees genom att hitta det tillräckliga och i värsta fall nödvändiga antalet experiment som forskaren måste utföra för att upptäcka den sanna CStree bland p variabler. Vi generaliserar spelets teoretiska tillvägagångssätt som presenteras i Eberhardts papper, till CStrees med en specificerad kausal ordning. Vi ger också en geometrisk beskrivning av kontextspecifika hårda ingripanden i CStrees, genom ett bijection mellan stadierna i CStree och ansikten på en polytop.

In this thesis we consider a set of mobile users that employ cloud-based computation offloading. In computation offloading, user energy consumption can be decreased by uploading and executing jobs on a remote server, rather than processing the jobs locally. In order to execute jobs in the cloud however, the user uploads must occur over a base station channel which is shared by all of the uploading users. Since the job completion times are subject to hard deadline constraints, this restricts the feasible set of jobs that can be remotely processed, and may constrain the users ability to reduce energy usage. The system is modelled as a competitive game in which each user is interested in minimizing its own energy consumption. The game is subject to the real-time constraints imposed by the job execution deadlines, user specific channel bit rates, and the competition over the shared communication channel. The thesis shows that for a variety of parameters, a game where each user independently sets its offloading decisions always has a pure Nash equilibrium, and a Gauss-Seidel method for determining this equilibrium is introduced. Results are presented which illustrate that the system always converges to a Nash equilibrium using the Gauss-Seidel method. Data is also presented which show the number of Nash equilibria that are found, the number of iterations required, and the quality of the solutions. We find that the solutions perform well compared to a lower bound on total energy performance. / Thesis / Master of Applied Science (MASc)

In this dissertation, we study several quantitative approaches centered on supply chain management, sustainability development, performance measurement frameworks, and environmental regulation mechanisms. The topic of sustainability has been of great interest for the past few years in academia. Many governments also have taken actions to incentivize firms to reduce their negative environmental and social impacts. It is unclear, however, how successful policy makers have been in reducing the sustainability threats. This raises the question of ``how can policy makers play an effective role in helping businesses become more sustainable, while complying with entrepreneurs and investors' expectations?'' This dissertation is organized on the basis of six chapters. Having reviewed the literature and research directions of sustainable supply chain management in Chapter 1, we present a review of sustainability performance measurement frameworks in Chapter 2. In addition to proposing a framework to assess sustainability efficiency in supply chains, we discuss research questions with a focus on the social aspect of sustainability development. In Chapter 3, we develop a two-stage data envelopment analysis model with an application to the energy sector. This approach measures relative efficiencies of a number of comparable decision makers and does not require predetermined weights of indicators. We relax some restricting assumptions used in previous studies and obtain a nonlinear problem, for which we develop a solution method. Chapter 4 investigates a more general multi-stage assessment framework that monitors suppliers, manufacturers, distributers, and retailers' sustainable practices. The major finding is developing a multi-stage data envelopment analysis to measure supply chains' sustainability efficiency. In Chapter 5, we investigate market-based schemes with a focus on curbing pollution emitted by business entities and develop a game-theoretic formulation. Finally, we summarize the major contributions of this dissertation and future research directions in Chapter 6. / Thesis / Doctor of Philosophy (PhD)