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This dissertation explores the importance of the payoff structure and beliefs for noncooperative games. Chapter 2 considers instances where the payoffs and the objectives may not be very clear to the players or the analyst. We develop a model for analyzing such games using a vector of reference utilities which are included in the definition of the game and assumed to be shared by all players. These are used to obtain the true utilities in the game. Conditions for the existence of equilibrium are identified by allowing players to have beliefs about the others. The solution concept is applied to the Traveler's Dilemma and a duopoly. In Chapter 3 a non-cooperative model of network formation is developed. Agents form links based on the cost of the link and its assessed benefit. Link formation is one-sided, i.e., agents can initiate links with other agents without their consent, provided the agent forming the link makes the appropriate investment. The model builds on the work of Bala and Goyal, but allows for agent heterogeneity by allowing for different failure probabilities. We investigate Nash networks that exhibit connectedness and redundancy and provide an explicit characterization of star networks. Efficiency and Pareto-optimality issues are discussed through examples. We also explore the consequences of three alternative specifications which address criticisms of such communication networks. Chapter 4 examines noncooperative fuzzy games. Both in fuzzy noncooperative games and in abstract economies, players impose mutual restrictions on their available strategic choices. Here we combine these two theories: A player tries to minimize the restrictions he imposes on others, while respecting the restrictions imposed by others on him, but does not explicitly pursue any other objectives of his own. We establish existence of an equilibrium in this framework. In Chapter 5 normal form game is modeled using tools from fuzzy set theory. We extend the decision theory framework of Bellman and Zadeh (1970) to a game-theoretic setting. The formulation is preliminary / Ph. D.

This dissertation consists of three essays, of which, two involve assessing the value of tree cover in urban communities and the other evaluates cooperative management of an invasive species by urban communities. The first chapter summarizes the three topics and briefly describes the motivation, methods applied and main conclusions in each study. Chapter 2 presents a meta-analysis of hedonic property value studies on the value of tree cover. A meta-regression was performed using implicit value estimates for tree cover at property-level from various locations in the U.S. along with auxiliary data of county-level tree cover to investigate the relationship between tree cover and implicit-price estimates for residential properties. The study found that on average 35 percent and 40 percent tree cover respectively at property-level and county-level optimize the benefits to the property owners in urban areas. These results provide insights to forward-looking communities to adapt their tree planting and protection efforts to lessen climate-induced impacts. Chapter 3 applies a first-stage Hedonic property price model to estimate preference for tree cover in urban communities using single-family house sales data from multiple property markets across the U.S. The study analyses how home owners' preference for tree cover vary across the landscape and across cities. Further, it identifies what factors affect these variations via the general inferences obtained from an internal meta-analysis. The study confirms the heterogeneity of preferences as affected by the differences in the abundance of tree cover in study locations, regional differences and household characteristics. These findings add to the hedonic literature and provide useful information for future urban planning. Chapter 4 focuses on cooperative management of invasive species in landscapes with mixed land ownerships. This study analyzes the effect of the land ownership on the management efforts between an infested municipality and an uninfested municipality when a transferable payment scheme is involved in the cooperative agreement. A dynamic optimization problem was set up to evaluate the case of Emerald ash borer (EAB) control in multiple jurisdictions in the Twin Cities, Minnesota. The results suggest that when the infested municipality has more public lands and when the transfer payments are efficiently used to implement greater control, the municipalities are more likely to commit to bargaining, and smaller transfer payments paid over a longer span of time are sufficient for optimal control of the spread of invasive species across the municipalities. The last chapter concludes the three studies and discusses the insights for future research. / Ph. D.

Increasing dynamics in power systems on account of renewable integration, electric vehicle penetration and rising demands have resulted in the exploration of energy storage for potential solutions. Recent technology- and industry-driven developments have led to a drastic decrease in costs of these storages, further advocating their usage. This thesis compiles the author's research on optimal integration of energy storage. Unpredictability is modelled using random variables favouring the need of stochastic optimization algorithms such as Lyapunov optimization and stochastic approximation. Moreover, consumer interactions in a competitive environment implore the need of topics from game theory. The concept of Nash equilibrium is introduced and methods to identify such equilibrium points are laid down. Utilizing these notions, two research contributions are made. Firstly, a strategy for controlling heterogeneous energy storage units operating at different timescales is put forth. They strategy is consequently employed optimally for arbitrage in an electricity market consisting of day-ahead and real-time pricing. Secondly, energy storages owned by consumers connected to different nodes of a power distribution grid are coordinated in a competitive market. A generalized Nash equilibrium problem is formulated for their participation in arbitrage and energy balancing, which is then solved using a novel emph{weighted} Lyapunov approach. In both cases, we design real-time algorithms with provable suboptimality guarantees in terms of the original centralized and equilibrium problems. The algorithms are tested on realistic scenarios comprising of actual data from electricity markets corroborating the analytical findings. / Master of Science

Nesse trabalho, aplicando métodos da Topologia Algébrica, nós obtivemos novas versões do teorema de equilíbrio de Nash. Nós definimos um conceito de equilíbrio local para jogos não cooperativos, o chamado equilíbrio local fraco, e demonstramos sua existência quando os espaços de estratégia são variedades diferenciáveis e as funções payoff são continuamente diferenciáveis. Nós demonstramos a ineficiência do equilíbrio local fraco no sentido de Pareto / In this work, applying methods of Algebraic Topology, we obtain new versions of the Nash equilibrium theorem. We define a concept of local equilibrium for non-cooperative games, the socalled weak local equilibrium, and we prove its existence when the spaces of strategies are differentiable manifolds and the payoff functions are continuously differentiable. We prove the ineffciency of weak local equilibrium in the Pareto sense

在各國職業運動的發展中，自由球員制度的出現醞釀出了大革命。本文以一賽局模型，利用Nash 議價及 Shapley 值等數學模型的輔助，嘗試探討自由球員制度出現後球員及球團效用的增減。最後，我們得到談判力量大小左右了勞資雙方談薪優勢或劣勢這樣的結果。當球團擁有高於球員的談判力量時，即使在自由球員制度下球團仍然獲益。

Les équations aux dérivées partielles (EDP) permettent d’aborder d’un point de vue mathématique des phénomènes observés dans tous les domaines des sciences. Certaines EDP non-linéaires modélisent des problèmes de mécanique statistique, mécanique des fluides, théories de la gravitation ou des mathématiques financières.L’objectif de ce travail de thèse est l’étude de certains problèmes d’ EDP non-linéaires et hamiltoniennes et la recherche des leurs solutions périodiques et quasi-périodiques. / The aim of this thesis is the research of periodic and quasi-periodic solutions for some non-linear hamiltonian PDEs.

Cette thèse étudie l’incorporation des préférences sociales typiques, telles que le souci de justice et la réciprocité, dans la chaîne logistique. Les impacts de ces préférences sociales sur la prise de décisions dans la chaîne logistique, sur l’efficacité et la coordination du canal de distribution sont étudiés. Plus spécifiquement, la thèse se focalise sur trois questions essentielles ci-dessous : 1. Qu’est-ce qui différencie un canal conventionnel d’un canal comportemental qui prend en compte la justice et/ou la réciprocité par exemple ? 2. Comment ces facteurs comportementaux influencent-ils la prise de décisions du fournisseur et du distributeur dans la chaîne logistique ? 3. Quels effets ont ces préférences sociales sur la coordination du canal de distribution et sur son efficacité ? Afin de répondre à ces questions, nous développons deux modèles d’opérations comportementales. Nous construisons d’abord un modèle de vendeur de journaux pour une chaîne logistique dyadique avec prise en compte de justice dans un processus de négociation de Nash. Dans ce modèle, un fournisseur joue un jeu de Stackelberg avec un distributeur qui doit faire face à une demande aléatoire. La solution de Nash est utilisèe comme référence de justice pour formellement décrire un compromis perçu comme juste, ce qui constitue une nouvelle manière de traiter la justice dans une chaîne logistique. Ensuite nous étudions un canal de distribution similaire mais où le fournisseur et le distributeur ont une préférence pour la réciprocité et la demande est supposée déterministe. Dans ce modèle, l’impact de l’intention dans une chaîne logistique est étudié pour la première fois. Des analyses approfondies de ces modèles comportementaux nous permettent de tirer des aperçus managériaux intéressants,comme par exemple le fait que le souci de justice joue un rôle important sur la difficulté de coordonner un canal de distribution. Nous avons démontré qu’un canal dyadique avec prise en compte de réciprocité peut être coordonné en utilisant un prix de gros constant, ce qui signifie que le problème de double marginalisation ne se pose pas nécessairement tout le temps. / This thesis studies how to incorporate typical social preferences, such as fairness concerns and reciprocity, into the context of supply chain. The impacts of theses social preferences on the supply chain’s decisions, channel efficiency and coordination are investigated. Specifically, it focuses on three important questions as follows: 1, what are the differences between the conventional channel and the behavioral channel (e.g., fairness-concerned channel and reciprocal channel)? 2, how do these behavioral factors influence the decisions of the supplier and the retailer in the supply chain? 3, what effects have these social preferences on the coordination of the channel and its efficiency? In order to answer these questions, two models of behavioral operations are formulated. A newsvendor model for a dyadic supply chain with Nash bargaining fairness concerns is built first. In this model, a supplier plays Stackelberg game with a retailer who faces stochastic demand. Nash bargaining solution is used as fairness reference to formally depict perceptively fair compromise, which is a new perspective to study fairness concerns in a supply chain. Then a similar dyadic channel in which a retailer and/or a supplier have a preference for reciprocity is investigated, but the retailer is facing deterministic demand. In this model, the impact of intention is studied within the context of supply chain for the first time. Some interesting and valuable managerial insights are drawn by analyzing the two behavioral models. For example, fairness concern does have great impact on the difficulty of coordinating a channel. In addition, the dyadic channel with reciprocity can be coordinated by using a constant wholesale price, which implies that the problem of double marginalization is not necessary to be present all the time.

Ce travail présente une optimisation bi-niveau pour la conception de réseaux durables de ressources dans les parcs éco-industriels (EIP). Tout d'abord, les méthodes d'optimisation multiobjectif sont explorées afin de gérer la nature multicritère des problèmes de conception de réseaux dans les EIP. Ensuite, différents cas d’étude sont explorés et analysés afin de maintenir un équilibre concernant les coûts opératoires des usines, tout en minimisant la consommation des ressources naturelles. Ainsi, le problème est modélisé selon une structure bi-niveau reprenant les concepts de la théorie des jeux, où les usines des entreprises jouent un jeu de Nash entre elles, tout en étant dans une structure de jeu de Stackelberg avec l'autorité environnementale. Cette structure définit un modèle qui doit être transformé en un problème MOPEC (Multiple Optimization Problems with Equilibrium Constraints). Différents cas d’étude sont explorés : le premier cas est le réseau d'eau mono-polluant d’un EIP dans lequel l’influence des paramètres opératoires des usines est étudiée afin de déterminer ceux qui favorisent la symbiose entre les usines. Le réseau d'eau est composé d'un nombre fixe de procédés et d’unités de régénération où les concentrations maximales d’entrée et de sortie des polluants sont définies a priori. L'objectif est alors de déterminer quelles sont les allocations entre procédés et unités de régénération. Les résultats obtenus mettent en évidence les avantages de la structure du modèle proposée par rapport aux approches multiobjectif traditionnelles, en obtenant des gains économiques équilibrés d’usines différentes (gains entre 12-25%) tout en maintenant une faible consommation globale des ressources. Ensuite, d'autres études de cas sont abordées à l'aide de la structure bi-niveau : il s’agit d'inclure simultanément les réseaux d'énergie et d’eau dans une formulation multileader multi-follower où les deux «autorités » environnementales sont supposées jouer un jeu non-coopératif de Nash. Dans un premier cas, le gain économique est plus important en incluant des réseaux d'énergie dans la structure de l’EIP. La deuxième étude de cas industriel explore un modèle de réseau d’utilités offre-demande où l'autorité environnementale vise à minimiser les émissions totales de CO2 dans le parc. La conclusion des différents cas explorés montre des résultats extrêmement favorables en termes de coût et d’impact environnemental ce qui vise à encourager les entreprises à participer à l'EIP. / This work presents a bilevel programming framework for the design of sustainable resource networks in eco-industrial parks (EIP). First, multiobjective optimization methods are explored in order to manage the multi-criteria nature of EIP network design problems. Then, different case studies are modeled in order to minimize and maintain in equilibrium participating plants operating costs while minimizing resource consumption. Thus, the structure of the model is constituted by a bilevel programming framework where the enterprises’ plants play a Nash game between them while being in a Stackelberg game structure with the authority. This structure defines a model which, in order to be solved, has to be transformed into a MOPEC (Multiple Optimization Problems with Equilibrium Constraints) structure. Regarding the case studies, monocontaminant water networks in EIP are studied first, where the influence of plants operating parameters are studied in order to determine the most important ones to favor the symbiosis between plants. The water network is composed of a fixed number of process and water regeneration units where the maximal inlet and outlet contaminant concentrations are defined a priori. The aim is to determine which processes are interconnected and the water regeneration allocation. Obtained results highlight the benefits of the proposed model structure in comparison with traditional multiobjective approaches, by obtaining equilibrate different plants operating costs (i.e. gains between 12-25%) while maintaining an overall low resource consumption. Then, other case studies are approached by using the bilevel structure to include simultaneously energy networks in a multi-leader-multi-follower formulation where both environmental authorities are assumed to play a noncooperative Nash game. In the first case study, economic gain is proven to be more significant by including energy networks in the EIP structure. The second industrial case study explores a supply-demand utility network model where the environmental authority aims to minimize the total equivalent CO2 emissions in the EIP. In all cases, the enterprises’ plants are encouraged to participate in the EIP by the extremely favorable obtained results.