Spectrum access protocols have been proposed recently to provide flexible and efficient use of the available bandwidth. Game theory has been applied to the analysis of the problem to determine the most effective allocation of the users’ power over the bandwidth. However, prior analysis has focussed on Shannon capacity as the utility function, even though it is known that real signals do not, in general, meet the Gaussian distribution assumptions of that metric. In a non-cooperative spectrum sharing environment, the Shannon capacity utility function results in a water-filling solution. In this thesis, the suitability of the water-filling solution is evaluated when using non-Gaussian signalling first in a frequency non-selective environment to focus on the resource allocation problem and its outcomes. It is then extended to a frequency selective environment to examine the proposed algorithm in a more realistic wireless environment. It is shown in both scenarios that more effective resource allocation can be achieved when the utility function takes into account the actual signal characteristics. Further, it is demonstrated that higher rates can be achieved with lower transmitted power, resulting in a smaller spectral footprint, which allows more efficient use of the spectrum overall. Finally, future spectrum management is discussed where the waveform adaptation is examined as an additional option to the well-known spectrum agility, rate and transmit power adaptation when performing spectrum sharing.

À l'ère de la mondialisation, l’environnement industriel et économique a subi plusieurs changements majeurs. Les chaînes logistiques sont en train de devenir de plus en plus de complexes réseaux composés de nombreux acteurs qui sont tantôt en concurrence et tantôt coopèrent pour répondre aux incessantes exigences des consommateurs. Dans un tel contexte, les entreprises se sont rapidement rendu compte de la limite du modèle complètement décentralisé où chacune d’entre elles optimise sa propre chaîne logistique indépendamment des autres acteurs. Afin de trouver de nouvelles sources de compétitivité et de faire face à la perpétuelle complexité de l’environnement économique, les entreprises tentent de dépasser la frontière des actions individuelles favorisant les actions coordonnées et centralisées. Désormais, la coopération entre les diverses chaînes logistiques et la formation d’alliances se trouvent au coeur des préoccupations des entreprises. En effet, en mutualisant les moyens logistiques, la coopération permet une meilleure exploitation des ressources et par le biais des actions collectives, elle permet de mieux bénéficier des économies d’échelles conduisant à réduire significativement les coûts et à générer des bénéfices considérables. Toutefois, dans de tels systèmes coopératifs, les acteurs sont indépendants et par ailleurs toujours intéressés en priorité par leurs profits individuels. De ce fait, la coopération soulève deux enjeux essentiels : (1) Quelles sont les alliances qui sont susceptibles de se former ? Et (2), comment partager les bénéfices réalisés sur les différents acteurs coopérants ? Dans cette thèse, nous nous intéressons au phénomène de la coopération dans les chaînes logistiques. Particulièrement, nous posons les précédentes questions dans des chaînes logistiques ou plusieurs firmes peuvent réduire leurs coûts logistiques en optant pour une gestion collective des stocks. Les principaux résultats de cette thèse portent sur l’utilisation des principes de la théorie des jeux coopératifs pour déterminer les alliances les plus profitables ainsi que la portion de profit que chaque firme doit recevoir afin de garder la stabilité des alliances formées. / In the age of outsourcing and globalization, the economic and industrial landscape has seen many radical changes. In such context, supply chains are becoming complex networks of a large number of entities that sometimes compete and sometimes cooperate to fulfill customers’ needs. Standalone supply chains, where each entity makes its decisions so as to maximize its own profits according to its own objectives, often lead to a loss of efficiency and fail to face the complexity of the economic environment they are facing with. Cooperative structures, however, where resources/service facilities are shared and decisions are made to maximize the global profit, prove to be more beneficial and efficient. Consequentially, many companies are fundamentally changing their way of doing business by exceeding the border of standalone and individual actions toward collective actions and cooperative strategies. Therefore, building alliances appears as a successful strategy in modern supply chain networks. In general, cooperation enables a better exploitation of the system’s resources and offers the opportunity to get benefit from large economies of scope, which in turn reduces the total cost/increases the total savings. However, it raises two natural questions that need to be addressed: (1) Which coalitions can be expected to be formed? And, (2) How will the cooperating actors share their total profit? In this Ph.D. dissertation, we tempt to address these questions in retail supply chains where independent retailers coordinate their replenishment from a supplier in order to save on delivery costs. Considering various joint replenishment environments, our principal contribution is to use principles from cooperative game theory to identify the most profitable alliances and to determine the portion of profit that would be allocated to each actor in order to guarantee the stability of the formed alliances.

Cooperation among humanitarian organizations has attracted increasing attention to enhance effectiveness and efficiency of relief supply chains. Our research focuses on horizontal cooperation in inventory management which is currently implemented in the United Nations Humanitarian Response Depot (UNHRD) network. The present work follows a two-step research approach, which involves collection of empirical data and quantitative modeling to examine and overcome the coordination challenges of the network. Our interviews with members of the network identified several managerial issues for sustainable cooperative inventory management that the UNHRD network pursues. Using a newsvendor model in the context of non-cooperative game theory, our research has explored member humanitarian organizations' incentive of joining the network, a coordination mechanism which achieves system optimality, and impacts of members' decisions about stock rationing. Our results indicate that behaviors of member HOs do not necessarily align with the UNHRD's expectation. Our results suggest that for system optimality, a system coordinator should carefully assess the circumstances, including demand coefficient and stock rationing. Our research also proposes a policy priority for the first-best system optimal inventory management.

Spectrum access protocols have been proposed recently to provide flexible and efficient use of the available bandwidth. Game theory has been applied to the analysis of the problem to determine the most effective allocation of the users’ power over the bandwidth. However, prior analysis has focussed on Shannon capacity as the utility function, even though it is known that real signals do not, in general, meet the Gaussian distribution assumptions of that metric. In a non-cooperative spectrum sharing environment, the Shannon capacity utility function results in a water-filling solution. In this thesis, the suitability of the water-filling solution is evaluated when using non-Gaussian signalling first in a frequency non-selective environment to focus on the resource allocation problem and its outcomes. It is then extended to a frequency selective environment to examine the proposed algorithm in a more realistic wireless environment. It is shown in both scenarios that more effective resource allocation can be achieved when the utility function takes into account the actual signal characteristics. Further, it is demonstrated that higher rates can be achieved with lower transmitted power, resulting in a smaller spectral footprint, which allows more efficient use of the spectrum overall. Finally, future spectrum management is discussed where the waveform adaptation is examined as an additional option to the well-known spectrum agility, rate and transmit power adaptation when performing spectrum sharing.

The diploma thesis describes design and creation of agent-based model of cooperative games and its subsequent analysis. The created model combines assumptions of game the-ory with other findings; it examines the dynamics of coalition formation and the influence of external and internal factors on this formation. The first theoretical part introduces the game theory and clarifies basic principles and con-cepts of N - player cooperative games. It evaluates the benefits and disadvantages of solu-tions introduced by this theory. The thesis further deals with multi-agent systems focused on agent-based models as an analytical and computational method for analyzing complex systems. There are also explained basic principles of agent-based modeling, including ap-proaches of their creation. Furthermore, there are presented distinctions between different types of agents, environments and models. The second practical part specifies assumptions and principles that are essential for the created multi-agent model. The diploma thesis describes the development of agent-based model of cooperative games by itself, including its characteristics and behavior. Final analysis of the created model clarifies impact of individual variables on the coalition for-mation process and confirms its ability to investigate given area.

The Cooperative Game Theory is a scientific discipline which offers rich mathematical apparatus for describing complex situations in the social reality. Its apparatus includes an extension to hierarchical structures and therefore can be applied to numerous research problems from the International Relations field. However, a cooperative game theoretical approach is very scarcely used. The main goal of the diploma thesis is to demonstrate, on the research problem of decision making in participation in local conflicts, the benefits of results that can be achieved by the application of the Cooperative Game Theory. In the first part of the thesis, theoretical foundations are laid and basic concepts are introduced. The second part is focused on forming a series of models of cooperative games with hierarchical structures from four local conflict situations, which are subsequently restricted in order to describe authoritative relations in structure. Restricted games are solved, the results are interpreted and evaluation of how these results can contribute to addressing the research problem follows.

Shale gas has emerged as a potential resource to transform the global energy market. Nevertheless, gas extraction from tight shale formations is only possible after horizontal drilling and hydraulic fracturing, which generally demand large amounts of water. Part of the ejected fracturing fluid returns to the surface as flowback water, containing a variety of pollutants. Thus, water reuse and water recycling technologies have received further interest for enhancing overall shale gas process efficiency and sustainability. Thereby, the objectives of this thesis are: - Develop mathematical models to treat flowback and produced water at various salinities and flow rates, decreasing the high environmental impact due to the freshwater withdrawal and wastewater generated during shale gas production at minimum cost. - Develop mathematical programming models for planning shale gas water management through the first stage of the well's life to promote the reuse of flowback water by optimizing simultaneously all operations belonging several wellpads. Within the first objective, we developed medium size generalized disjunctive-programming (GDP) models reformulated as mixed integer non-linear programming problems (MINLPs). First, we focused on flowback water pretreatment and later, in wastewater desalination treatment. Particularly, an emergent desalination technology, Membrane Distillation, has been studied. All mathematical models have been implemented using GAMS® software. First, we introduce a new optimization model for wastewater from shale gas production including a superstructure with several water pretreatment alternatives. The mathematical model is formulated via GDP to minimize the total annualized cost. Hence, the superstructure developed allows identifying the optimal pretreatment sequence with minimum cost, according to inlet water composition and wastewater desired destination (i.e., water reuse as fracking fluid or desalination in thermal or membrane techonologies). As each destination requires specific composition constraints, three case studies illustrate the applicability of the proposed approach. Additionally, four distinct flowback water compositions are evaluated for the different target conditions. The results highlight the ability of the developed model for the cost-effective water pretreatment system synthesis, by reaching the required water compositions for each specified destination. Regarding desalination technologies, a rigorous optimization model with energy recovery for the synthesis of multistage direct contact membrane distillation (DCMD) system has been developed. The mathematical model is focused on maximizing the total amount of water recovered. The outflow brine is fixed close to salt saturation conditions (300 g·kg-1) approaching zero liquid discharge (ZLD). A sensitivity analysis is performed to evaluate the system’s behavior under different uncertainty sources such as the heat source availability and inlet salinity conditions. The results emphasize the applicability of this promising technology, especially with low steam cost or waste heat, and reveal variable costs and system configurations depending on inlet conditions. Within the second objective, large-scale multi-period water management problems, and collaborative water management models have been studied. Thus, to address water planning decisions in shale gas operations, in a first stage a new non-convex MINLP optimization model is presented that explicitly takes into account the effect of high concentration of total dissolved solids (TDS) and its temporal variations in the impaired water. The model comprises different water management strategies: direct reuse, treatment or send to Class II disposal wells. The objective is to maximize the “sustainability profit” to find a compromise solution among the three pillars of sustainability: economic, environmental and social criteria. The solution determines freshwater consumption, flowback destination, the fracturing schedule, fracturing fluid composition and the number of tanks leased at each time period. Because of the rigorous determination of TDS in all water streams, the model is a nonconvex MINLP model that is tackled in two steps: first, an MILP model is solved on the basis of McCormick relaxations for the bilinear terms; next, the binary variables that determine the fracturing schedule are fixed, and a smaller MINLP is solved. Finally, several case studies based on Marcellus Shale Play are optimized to illustrate the effectiveness of the proposed formulation. Later, a simplified version of the shale gas water management model developed in the previous work has been used to study possible cooperative strategies among companies. This model allows increasing benefits and reduces costs and environmental impacts of water management in shale gas production. If different companies are working in the same shale zone and their shale pads are relatively close (under 50 km), they might adopt a cooperative strategy, which can offer economic and environmental advantages. The objective is to compute a distribution of whatever quantifiable unit among the stakeholders to achieve a stable agreement on cooperation among them. To allocate the cost, profit and/or environmental impact among stakeholders, the Core and Shapley value are applied. Finally, the impact of cooperation among companies is shown by two examples involving three and eight players, respectively. The results show that adopting cooperative strategies in shale water management, companies are allowed to improve their benefits and to enhance the sustainability of their operations. The results obtained in this thesis should help to make cost-effective and environmentally-friendly water management decisions in the eventual development of shale gas wells.

Diese Dissertation präsentiert Modelle zur Lösung von Verhandlungsproblemen mit diskreten Strukturen. Hauptgrundlage der Betrachtung ist dabei die Erweiterung und Anwendung von Theorien der kooperativen Spieltheorie. Insbesondere der Shapley-Wert spielt eine wichtige Rolle. Als erste Problemklasse werden kooperative Spiele präsentiert, bei denen einige Spiele feste Auszahlungen erhalten. Als zweite Problemklasse werden kooperative Spiele untersucht, deren Lösungen ausschließlich ganzzahlig sein dürfen.

[pt] O objetivo desta dissertação é analisar a aplicação de metodologias de alocação de capacidade firme de usinas termelétricas através da teoria dos jogos cooperativos e suas conseqüências na cooperação entre os agentes. Mostra-se que não existe uma maneira ótima, única, de se fazer esta repartição, mas existem critérios para verificar se uma metodologia de repartição específica apresenta algum aspecto inadequado. Um desses critérios é a justiça. Mostra-se que este sentido de justiça equivale a pertencer ao chamado núcleo de um jogo cooperativo, onde não há subsídio de um subgrupo por outro. O cálculo da capacidade firme ou Capacidade de Suprimento de Carga será formulado como um problema de otimização linear e serão investigadas vantagens e desvantagens de distintos métodos de alocação (benefícios marginais, última adição, Nucleolus, Shapley). A aplicação desses métodos tem um crescimento exponencial de esforço computacional, o método de Aumann- Shapley abordado em seguida fornece para o problema de alocação de capacidade firme uma solução computacional mais eficiente, embora em sua descrição aparentemente o método aumente o esforço computacional. Em seguida foram realizados resultados numéricos com sistemas genéricos de pequeno porte. / [en] The objective of this work is to investigate the application of different methodologies of allocation of firm capacity rights among thermal plants using a game-theoretic framework and the consequences in the cooperation among the agents. It is shown that there is not an optimal and unique approach to make this allocation but there are criteria to verify if a given approach presents any inadequate aspect. One of these criteria is the justice, or fairness. It is shown that a one sense of justice is equivalent to the condition of the core of a cooperative game. The calculation of the firm capacity will be formulated as a linear program and advantages/disadvantages of different allocation methods (marginal allocation, incremental allocation, Nucleolus, Shapley) will be investigated. The complexities of these methods are exponential, so it will be shown that the Aumann-Shapley (AS) scheme to the problem of allocation of capacity rights will be more efficient. Numerical results about the difference allocations in these methods are presented in general smalls systems.

Complex economic activity often involves inter-relationships at several levels of production, often referred to as supply chains or procurement networks. In this thesis we address the problem of forming procurement networks for items with value adding stages that are linearly arranged. Formation of such procurement networks involves a bottom-up assembly of complex production, assembly, and exchange relationships through supplier selection and contracting decisions. Recent research in supply chain management has emphasized that such decisions need to take into account the fact that suppliers and buyers are intelligent and rational agents who act strategically. Game theory has therefore emerged as a crucial tool for supply chain researchers to model, analyze, and design supply chains that are both efficient and stable. In this thesis, we explore cooperative game theory as a framework to model and analyze the formation of efficient and stable procurement networks. We view the problem of Procurement Network Formation (PNF) for multiple units of a single item as a cooperative game where agents cooperate to form a surplus maximizing procurement network and then share the surplus in a fair manner. We address this problem in three different informational settings: (a) Complete information environments, (b) Incomplete but non-exclusive information environments and (c) Incomplete information environments. In the complete information case, we first investigate the use of the core as a solution concept. We show the structural conditions under which the core is non-empty. We then provide an extensive form game that implements the core in sub-game perfect Nash equilibrium whenever the core is non-empty. Secondly, we examine the implications of using the Shapley value as a solution concept for the game when the buyer is also included as a game theoretic agent. Analogous to the mechanism that implements the core, we adapt and construct an extensive form game to implement the Shapley value of the game. In the incomplete but non-exclusive information case, we focus on the incentive compatible coarse core as an appropriate solution concept and show its non-emptiness for the PNF game. In the incomplete information case, we focus on the incentive compatible fine core as an appropriate solution concept and show its non-emptiness for the PNF game. We believe the thesis establishes cooperative game theory as an extremely effective tool to model and solve the procurement network formation problem. 1