Il existe de nombreuses méthodes d'optimisation du routage réseau en général. Dans cette thèse nous nous intéressons au développement d'algorithmes distribués permettant une stabilisation, au sens de Nash, des flux réseaux. Nous rappelons tout d'abord brièvement le contexte général d'Internet aujourd'hui et quelques notions de théorie des jeux. Nous présentons un jeu de tarification simple à deux joueurs, que la méthode des joueurs fictifs permet de faire converger. Puis nous présentons un jeu de routage plus complexe, à n joueurs, basé sur le modèle de Wardrop, ainsi qu'un algorithme de comportement distribué qui permet au système de converger vers un équilibre de Wardrop (équilibre social). Ces équilibres sont confondus avec les équilibres de Nash dans le cas limite où un joueur représente une partie infinitésimale du trafic. Nous présentons ensuite un raffinement de notre représentation initiale du problème, qui permet une diminution de sa complexité, en terme de dimension des espaces de stratégies et de temps de calcul. Nous montrons qu'il s'agit d'une bonne heuristique d'approximation de la première méthode trop coûteuse, sa qualité dépend d'un unique paramètre. Enfin, nous concluons par la présentation de résultats de simulation qui montrent que notre méthode distribuée est effectivement capable d'apprendre les meilleurs équilibres du système. / There are several approaches for optimizing network routing in general. In this document, we are interested in developping distributed algorithms able to stabilize the network flows in the sense of Nash. We introduce the general context of the Internet today along with a few key-notions in game theory. We show a simple two-player tarification game that the fictitious player dynamics is able to solve. Then, we introduce a more complex routing game with n players based on the Wardrop model and a distributed learning algorithm that allows the system to converge towards Wardop equilibria (social equilibrium). These equilibria also are Nash equilibria in the limit case where a player is an infinitesimal part of the network flow. We present a refinement of our initial representation of the problem that narrows down its complexity, in terms of the size of the strategy space and computation time. We show that it is a good heuristic for approximating the previous method, its quality relies upon only one parameter. Finally, we conclude with simulations results, showing that our distributed method is able to learn the best equilibriua of the system.

O mercado automotivo global em 2008 sofreu uma queda drástica na produção e nas vendas após a eclosão da crise do subprime nos Estados Unidos. Em todo o mundo, políticas de fomento foram sendo implementadas sob as mais variadas formas para recuperar o setor. Presumivelmente, em resposta à crise, o governo brasileiro resolveu agir decretando a política anticíclica de redução do IPI ao mercado automobilístico em 2008, sendo está repetida em 2012. Neste mesmo ano também ocorreu a modificação do acordo automotivo Brasil/México, e em 2013 foi implantado o INOVAR-AUTO. Sendo assim, o objetivo do presente estudo, será avaliar o efeito da diminuição do IPI sobre o comportamento da demanda, da oferta e os efeitos líquidos sobre os agentes de mercado. O estudo se relaciona com uma literatura que busca avaliar os efeitos de reformas tributárias em indústrias com produtos diferenciados, como Fershtman, Gandal e Markovich (1999) e Verboven (2002). É empregado o modelo logit aninhado de McFadden et al. (1973) e estendido por Berry (1994), combinado com uma estrutura de competição oligopolista pressupondo equilíbrio nos preços, segundo Nevo (1998), do tipo Nash-Bertrand. Adicionalmente, é elaborado uma análise econométrica preliminar de preços hedônicos, seguindo Griliches (1961), formulado num painel de efeitos fixos que avaliará o comportamento dos preços médios dos veículos novos nos períodos de modificação do IPI. Os resultados dos modelos de apreçamento hedônico demonstram que as montadoras não remanejaram os preços médios no mesmo percentual efetivo da queda do IPI. As variações dos preços foram mais baixas do que a da alíquota. Na metodologia discreta, os resultados apontam que empresas que detém maiores poderes de mercado possuem elasticidades preço próprias baixas. Lucros mais elevados estão associados a marcas que no grosso de suas vendas comercializam automóveis de menor porte que embutem uma alta relação markup preço-custo. Montadoras nacionais tiveram melhor desempenho que suas contrapartes importadoras. A carga tributária altíssima é o principal vilão para o desempenho ruim dos importados. Os excedentes gerados com a modificação do IPI foram positivos para todos os agentes. Consumidores, produtores e governo ganharam com a medida. Ou seja, há espaço para reduções de impostos com aumento da arrecadação do governo. / The global automotive market in 2008 saw a sharp drop in production and sales following the outbreak of the subprime crisis in the United States. Throughout the world, development policies have been implemented in a variety of ways to recover the sector. Presumably, in response to the crisis, the Brazilian government decided to act by decreeing the anti-cyclical policy of reducing the IPI to the automobile market in 2008, and is repeated in 2012. In 2012 also occurred the modification of the automotive agreement Brazil / Mexico, and in 2013 was implanted the INOVAR-AUTO. Therefore, the objective of the present study will be to evaluate the effect of the reduction of IPI on the behavior of demand, supply and net effects on market agents. The study is related to a literature that seeks to evaluate the effects of tax reforms in industries with differentiated products, such as Fershtman, Gandal e Markovich (1999) and Verboven (2002). The nested logit model of McFadden et al. (1973) and extended by Berry (1994), combined with an oligopolistic competition structure presupposing price equilibrium, according to Nevo (1998), of the Nash-Bertrand type, is used. Additionally, a preliminary econometric analysis of hedonic prices is elaborated, following Griliches (1961), formulated in a panel of fixed effects that will evaluate the behavior of the average prices of new vehicles in the periods of modification of the IPI. The results of the hedonic pricing models show that the automakers did not change average prices in the same effective percentage of the IPI fall. Price changes were lower than the rate. In the discrete methodology, the results indicate that companies that have greater market power have lower price elasticities. Higher profits are associated with brands that in the bulk of their sales market smaller automobiles that embody a high price-cost markup ratio. National car manufacturers performed better than their importing counterparts. The very high tax burden is the main villain for the poor performance of imported. The surpluses generated with the IPI change were positive for all agents. Consumers, producers and government won with the measure. That is, there is room for tax cuts with increased government revenue.

Neste trabalho demonstram-se os teoremas de ponto fixo de Brouwer e Kakutani com o objetivo de provar a existência do equilíbrio de Nash em jogos finitos em forma normal. No primeiro capítulo apresentam-se as definições de teoria dos jogos, começando com jogos finitos em forma normal e terminando com o conceito de equilíbrio de Nash. Na primeira seção do capítulo dois desenvolve-se a teoria de simplexes, em Rn, e se demonstra o teorema de Brouwer. Na seção seguinte, são relacionadas as propriedades de semi-continuidade superior e gráfico fechado em set functions, para então provar os teoremas de Celina e von Neumann que, em conjunto com o teorema de Brouwer, resultam no teorema de Kakutani no fim da seção. Como último resultado é demonstrado o teorema de existência do equilíbrio de Nash em jogos finitos em forma normal através do teorema de Kakutani, mostrando que o equilíbrio de Nash é um ponto fixo de uma set function. / In this work, the fixed-point theorems of Kakutani and Brouwer are proved with the intention of showing the existence of Nash equilibrium in finite normal-form games. In the first chapter the needed definitions of game theory are shown, starting with finite normal-form games and ending with the concept of Nash equilibrium. In the first section of chapter two, simplex theory in Rn is developed and then the Brouwer fixer point theorem is proved. In the next section, some relations of upper hemi-continuity and closed graph in set functions are shown, then proving the theorems of Celina and von Neumann that, along with Brouwer theorem, result in Kakutani fixed-point theorem in the end of the section. As the last result, the existence of Nash equilibrium in finite normal-form games is proved through Kakutani’s theorem, relating the Nash equilibrium to the fixed-point of a set function.

This thesis deals with factors which are important for making decisions in the game of poker. The goal is to find a way to improve players chances of success in this game. The first two chapters describe the rules of poker and the basics and presumptions of the game theory The following chapters analyze some mathematical models and assumptions for applying these models in the game. These models should find the optimal solution for individuals in decision making situations. It can be considered a static situation, where the behavior of each player is predetermined and the decision maker tries to find an appropriate strategy. It is also can be considered a dynamic situation, when all players react to each other, which heads to equilibrium solution. As a consequence of rising popularity of poker tournaments many strategy books have appeared, as well as analytic software. Nevertheless, it is and probably will remain impossible to solve all decision situations which can occur. A very important factor of success are some gamblers attitude, experience and mental skills. Mathematical knowledge, however, will become more and more important. This thesis will help to understand the basic of mathematic models and their application in poker game.

Participants in deregulated electric power markets compete for financial transmission rights (FTRs) to hedge against losses due to transmission congestion by submitting bids to the independent system operator (ISO). The ISO obtains an FTR allocation, that maximizes sales revenue while satisfying simultaneous feasibility. This FTR allocation remains in place for a length of time during which the participants compete in the energy market to maximize their total payoff from both FTR and energy markets. Energy markets (bi-lateral, day ahead, real time) continue until the the end of the current FTR period, at which time the participants can choose to modify their FTR holdings for the next FTR period. As in any noncooperative game, finding Nash equilibrium bidding strategies is of critical importance to the participants in both FTR and energy markets. In this research, a two-tier matrix game theoretic modeling approach is developed that can be used to obtain equilibrium bidding behavior of the participants in both FTR and energy markets considering the total payoff from FTR and energy. The matrix game model presents a significant deviation from the bilevel optimization approach commonly used to model FTR and energy allocation problems. A reinforcement learning (RL) algorithm is also developed which uses a simulation model and a value maximization approach to obtain the equilibrium bidding strategies in each market. The model and the RL based solution approach allow consideration of multi-dimensional bids (for both FTR and energy markets), network contingencies, varying demands, and many participants. The value iteration based RL algorithm obtains pure strategy Nash equilibrium for FTR and energy allocation. A sample network with three buses and four participants is considered for demonstrating the viability of the game theoretic model for FTR market. A PJM network example with five buses, five generators and three loads is also considered to analyze equilibrium bidding behavior in joint FTR and energy markets. Several numerical experiments on the sample networks are conducted using the approach of statistical design of experiments (DOE) to assess impacts of variations of bid and network parameters on the market outcomes like participant payoffs and equilibrium strategies.

In this study cost-benefits problems concerning the knapsack problem of limited resources is studied and how this relates to an attacker perspective when choosing defense strategies. This is accomplished by adopting a cost-benefit method and merging it with game theory. The cost-benefit method chosen for this study is the Analytical Hierarchy Process and from the field of game theory the Bayesian Nash Equilibrium is used. The Analytical Hierarchy Process allows the user to determine internally comparable weights between elements, and to bring in a security dimension to the Analytical Hierarchy Process a sub category consisting of confidentiality, integrity and availability is used. To determine the attacker strategy and, in effect, determine the best defense strategy the Bayesian Nash Equilibrium is used.

Le contexte étudié est celui d'un système irrigué qui connaît une pénurie en eau structurelle. La thèse compare différentes règles d'allocation de l'eau et de taxation lorsqu'on tient compte des inévitables marges de manoeuvre dont disposent les irrigants, notamment en ce qui concerne la surface mise en culture, l'équipement ou la stratégie d'irrigation. Ces marges de manoeuvre peuvent engendrer une interdépendance entre les agriculteurs : les interactions qui en découlent sont déterminées à l'équilibre. De façon très générale, on peut définir des règles d'allocation de type ex ante, où chaque agriculteur reçoit une quantité d'eau indépendante de ses choix et de ceux des autres agriculteurs, et des règles de type ex post qui distribuent l'eau en fonction des choix effectués. Si les règles de type ex post permettent de bien valoriser l'eau sur l'ensemble du système irrigué et peuvent organiser un partage efficace du risque, elles créent aussi par la même occasion des interactions stratégiques qui aboutissent à un sur-assolement. Une comparaison est faite entre règles ex ante et ex post, avec des agriculteurs qui n'ont pas la même capacité à valoriser l'eau lorsque la ressource à partager est connue, et avec des agriculteurs d'aversions au risque différentes lorsque la ressource est incertaine. De plus, quand le coût d'audit du respect des allocations est important, le gestionnaire doit mettre en regard l'acquisition de plus d'information pour diminuer l'iportance de ces interactions, et le coût d'acquisition de cette information. Ces questions sont appliquées sur deux terrains d'étude: de petits périmètres irrigués en Tunisie centrale gérés par des associations d'irriguants, et le bassin de l'Adour dans le Sud-Ouest de la France, où la culture intensive du maïs provoque des tensions sur la ressource pendant l'été.

Avec les codes de calculs généralistes de la mécanique il est possible de suivre numériquement l'évolution de structures soumises a un chargement variable, avec des conditions aux bords classiques. Un des outils pour ces méthodes numériques (dites de continuation) est le théorème des fonctions implicites C1. Mais dans le cas des problèmes de contact avec ou sans frottement cet outil ne s'applique plus, car la solution n'est en général plus dérivable par rapport aux paramètres du problème. La difficulté a été surmontée pour les opérateurs semi-lineaires d'ordre 2 (cas d'une membrane élastique en grandes déformations), mais pas encore pour les plaques. Pour cela, nous avons généralise au bilaplacien le Théorème de stabilité de Schaeffer valable pour le laplacien. Ce qui fournit la dérivée de la frontière libre par rapport aux forces extérieures de classe C^infini, si la frontière libre est C^infini. Nous savons qu'il existe une dérivée par rapport aux forces de classe L2 de la solution pour le problème d'obstacle d'une poutre et d'une plaque élastique, avec des hypothèses sur la zone de contact assurant la polyédricité. Nous explorons l'analyse de sensibilité du problème de l'obstacle pour une poutre et une plaque linéaire, par des méthodes nouvelles d'analyse par perturbation au second ordre. Enfin nous expliquons comment ces résultats pourraient servir a comprendre la stabilité et la sensibilité des plaques de von Karman.

We propose a new classification for multi-agent learning algorithms, with each league of players characterized by both their possible strategies and possible beliefs. Using this classification, we review the optimality of existing algorithms and discuss some insights that can be gained. We propose an incremental improvement to the existing algorithms that seems to achieve average payoffs that are at least the Nash equilibrium payoffs in the long-run against fair opponents. / Singapore-MIT Alliance (SMA)

This thesis considers resource management issues in wireless sensor networks (WSNs), wireless local area networks (WLANs), and cognitive radio (CR) networks. Since energy is a critical resource in WSNs, we consider energy minimization techniques based on explicit node cooperation and distributed source coding (DSC). The explicit node cooperation based on space time block codes (STBC) improves energy efficiency of WSNs, by reducing the energy consumption per bit of each sensor node. The DSC on the other hand exploits the spatial correlation in WSNs, and thus reduces the data generated in a WSN. For the purpose of our analysis, we model the spatial correlation according to a linear Gauss-Markov model. Through our numerical results, we observe that the node cooperation combined with DSC can improve energy efficiency for many cases of interest. A unique aspect of our work is we obtain important structural results using the concepts from monotone comparative statics. These structural results provide insights into the general design of WSNs. Through our numerical results, we also demonstrate that, the cooperation based transmission can achieve better mutual information (MI)-energy tradeoff than the non-cooperation based transmission scheme. From the perspective of WLANs, we propose a price based approach to regulate the channel occupancy of low rate users, which is known to be the primary cause for low overall throughput in WLANs. Owing to the decentralized nature of WLANs we use non-cooperative game theory as a tool for analysis. Specifically, we use supermodular game theory. Through our analysis, we show that an increase in price leads to an increase in rate of WLAN users. We also prove that the best response dynamics indeed converge to the Nash equilibrium of the underlying non-cooperative game. Through our numerical results, we demonstrate that by proper tuning of the price, the proposed price based approach can lead to an improvement in overall throughput of a WLAN. Finally from the perspective of CR networks, we consider the impact of number of channels captured by a secondary user on its transmission control protocol (TCP) throughput. From our simulation results it was found that, there exists a definite optimal number of channels a secondary user needs to capture, to maximize its TCP throughput.