El mundo de las telecomunicaciones está cambiando de un escenario donde únicamente las personas estaban conectadas a un modelo donde prácticamente todos los dispositivos y sensores se encuentran conectados, también conocido como Internet de las cosas (IoT), donde miles de millones de dispositivos se conectarán a Internet a través de conexiones móviles y redes fijas. En este contexto, hay muchos retos que superar, desde el desarrollo de nuevos estándares de comunicación al estudio de la viabilidad económica de los posibles escenarios futuros. En esta tesis nos hemos centrado en el estudio de la viabilidad económica de diferentes escenarios mediante el uso de conceptos de microeconomía, teoría de juegos, optimización no lineal, economía de redes y redes inalámbricas. La tesis analiza la transición desde redes centradas en el servicio de tráfico HTC a redes centradas en tráfico MTC desde un punto de vista económico. El primer escenario ha sido diseñado para centrarse en las primeras etapas de la transición, en la que ambos tipos de tráfico son servidos bajo la misma infraestructura de red. En el segundo escenario analizamos la siguiente etapa, en la que el servicio a los usuarios MTC se realiza mediante una infraestructura dedicada. Finalmente, el tercer escenario analiza la provisión de servicios basados en MTC a usuarios finales, mediante la infraestructura analizada en el escenario anterior. Gracias al análisis de todos los escenarios, hemos observado que la transición de redes centradas en usuarios HTC a redes MTC es posible y que la provisión de servicios en tales escenarios es viable. Además, hemos observado que el comportamiento de los usuarios es esencial para determinar la viabilidad de los diferentes modelos de negocio, y por tanto, es necesario estudiar el comportamiento y las preferencias de los usuarios en profundidad en estudios futuros. Específicamente, los factores más relevantes son la sensibilidad de los usuarios al retardo en los datos recopilados por los sensores y la cantidad de los mismos. También hemos observado que la diferenciación del tráfico en categorías mejora el uso de las redes y permite crear nuevos servicios empleando datos que, de otro modo, no se aprovecharían, lo cual nos permite mejorar la monetización de la infraestructura. También hemos demostrado que la provisión de capacidad es un mecanismo válido, alternativo a la fijación de precios, para la optimización de los beneficios de los proveedores de servicio. Finalmente, se ha demostrado que es posible crear roles específicos para ofrecer servicios IoT en el mercado de las telecomunicaciones, específicamente, los IoT-SPs, que proporcionan servicios basados en sensores inalámbricos utilizando infraestructuras de acceso de terceros y sus propias redes de sensores. En resumen, en esta tesis hemos intentado demostrar la viabilidad económica de modelos de negocio basados en redes futuras IoT, así como la aparición de nuevas oportunidades y roles de negocio, lo cual nos permite justificar económicamente el desarrollo y la implementación de las tecnologías necesarias para ofrecer servicios de acceso inalámbrico masivo a dispositivos MTC. / The communications world is moving from a standalone devices scenario to a all-connected scenario known as Internet of Things (IoT), where billions of devices will be connected to the Internet through mobile and fixed networks. In this context, there are several challenges to face, from the development of new standards to the study of the economical viability of the different future scenarios. In this dissertation we have focused on the study of the economic viability of different scenarios using concepts of microeconomics, game theory, non-linear optimization, network economics and wireless networks. The dissertation analyzes the transition from a Human Type Communications (HTC) to a Machine Type Communications (MTC) centered network from an economic point of view. The first scenario is designed to focus on the first stages of the transition, where HTC and MTC traffic are served on a common network infrastructure. The second scenario analyzes the provision of connectivity service to MTC users using a dedicated network infrastructure, while the third stage is centered in the analysis of the provision of services based on the MTC data over the infrastructure studied in the previous scenario. Thanks to the analysis of all the scenarios we have observed that the transition from HTC users-centered networks to MTC networks is possible and that the provision of services in such scenarios is viable. In addition, we have observed that the behavior of the users is essential in order to determine the viability of a business model, and therefore, it is needed to study their behavior and preferences in depth in future studios. Specifically, the most relevant factors are the sensitivity of the users to the delay and to the amount of data gathered by the sensors. We also have observed that the differentiation of the traffic in categories improves the usage of the networks and allows to create new services thanks to the data that otherwise would not be used, improving the monetization of the infrastructure and the data. In addition, we have shown that the capacity provision is a valid mechanism for providers' profit optimization, as an alternative to the pricing mechanisms. Finally, it has been demonstrated that it is possible to create dedicated roles to offer IoT services in the telecommunications market, specifically, the IoT-SPs, which provide wireless-sensor-based services to the final users using a third party infrastructure. Summarizing, this dissertation tries to demonstrate the economic viability of the future IoT networks business models as well as the emergence of new business opportunities and roles in order to justify economically the development and implementation of the new technologies required to offer massive wireless access to machine devices. / El món de les telecomunicacions està canviant d'un escenari on únicament les persones estaven connectades a un model on pràcticament tots els dispositius i sensors es troben connectats, també conegut com a Internet de les Coses (IoT) , on milers de milions de dispositius es connectaran a Internet a través de connexions mòbils i xarxes fixes. En aquest context, hi ha molts reptes que superar, des del desenrotllament de nous estàndards de comunicació a l'estudi de la viabilitat econòmica dels possibles escenaris futurs. En aquesta tesi ens hem centrat en l'estudi de la viabilitat econòmica de diferents escenaris per mitjà de l'ús de conceptes de microeconomia, teoria de jocs, optimització no lineal, economia de xarxes i xarxes inalàmbriques. La tesi analitza la transició des de xarxes centrades en el servici de tràfic HTC a xarxes centrades en tràfic MTC des d'un punt de vista econòmic. El primer escenari ha sigut dissenyat per a centrar-se en les primeres etapes de la transició, en la que ambdós tipus de tràfic són servits davall la mateixa infraestructura de xarxa. En el segon escenari analitzem la següent etapa, en la que el servici als usuaris MTC es realitza per mitjà d'una infraestructura dedicada. Finalment, el tercer escenari analitza la provisió de servicis basats en MTC a usuaris finals, per mitjà de la infraestructura analitzada en l'escenari anterior. Als paràgrafs següents es descriu amb més detall cada escenari. Gràcies a l'anàlisi de tots els escenaris, hem observat que la transició de xarxes centrades en usuaris HTC a xarxes MTC és possible i que la provisió de servicis en tals escenaris és viable. A més a més, hem observat que el comportament dels usuaris és essencial per a determinar la viabilitat dels diferents models de negoci, i per tant, és necessari estudiar el comportament i les preferències dels usuaris en profunditat en estudis futurs. Específicament, els factors més rellevants són la sensibilitat dels usuaris al retard en les dades recopilats pels sensors i la quantitat dels mateixos. També hem observat que la diferenciació del tràfic en categories millora l'ús de les xarxes i permet crear nous servicis emprant dades que, d'una altra manera, no s'aprofitarien, la qual cosa ens permet millorar la monetització de la infraestructura. També hem demostrat que la provisió de capacitat és un mecanisme vàlid, alternatiu a la fixació de preus, per a l'optimització dels beneficis dels proveïdors de servici. Finalment, s'ha demostrat que és possible crear rols específics per a oferir servicis IoT en el mercat de les telecomunicacions, específicament, els IoT-SPs, que proporcionen servicis basats en sensors inalàmbrics utilitzant infraestructures d'accés de tercers i les seues pròpies xarxes de sensors. En resum, en aquesta tesi hem intentat demostrar la viabilitat econòmica de models de negoci basats en xarxes futures IoT, així com l'aparició de noves oportunitats i rols de negoci, la qual cosa ens permet justificar econòmicament el desenrotllament i la implementació de les tecnologies necessàries per a oferir servicis d'accés inalàmbric massiu a dispositius MTC. / Sanchis Cano, Á. (2018). Economic analysis of wireless sensor-based services in the framework of the Internet of Things. A game-theoretical approach [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/102642 / TESIS

Parmi tous les jeux de société joués par les humains au cours de l’histoire, le jeu de go était considéré comme l’un des plus difficiles à maîtriser par un programme informatique [Van Den Herik et al., 2002]; Jusqu’à ce que ce ne soit plus le cas [Silveret al., 2016]. Cette percée révolutionnaire [Müller, 2002, Van Den Herik et al., 2002] fût le fruit d’une combinaison sophistiquée de Recherche arborescente Monte-Carlo et de techniques d’apprentissage automatique pour évaluer les positions du jeu, mettant en lumière le grand potentiel de l’apprentissage automatique pour résoudre des jeux. L’apprentissage antagoniste, un cas particulier de l’optimisation multiobjective, est un outil de plus en plus utile dans l’apprentissage automatique. Par exemple, les jeux à deux joueurs et à somme nulle sont importants dans le domain des réseaux génératifs antagonistes [Goodfellow et al., 2014] ainsi que pour maîtriser des jeux comme le Go ou le Poker en s’entraînant contre lui-même [Silver et al., 2017, Brown andSandholm, 2017]. Un résultat classique de la théorie des jeux indique que les jeux convexes-concaves ont toujours un équilibre [Neumann, 1928]. Étonnamment, les praticiens en apprentissage automatique entrainent avec succès une seule paire de réseaux de neurones dont l’objectif est un problème de minimax non-convexe et non-concave alors que pour une telle fonction de gain, l’existence d’un équilibre de Nash n’est pas garantie en général. Ce travail est une tentative d'établir une solide base théorique pour l’apprentissage dans les jeux. La première contribution explore le théorème minimax pour une classe particulière de jeux non-convexes et non-concaves qui englobe les réseaux génératifs antagonistes. Cette classe correspond à un ensemble de jeux à deux joueurs et a somme nulle joués avec des réseaux de neurones. Les deuxième et troisième contributions étudient l’optimisation des problèmes minimax, et plus généralement, les inégalités variationnelles dans le cadre de l’apprentissage automatique. Bien que la méthode standard de descente de gradient ne parvienne pas à converger vers l’équilibre de Nash de jeux convexes-concaves simples, il existe des moyens d’utiliser des gradients pour obtenir des méthodes qui convergent. Nous étudierons plusieurs techniques telles que l’extrapolation, la moyenne et la quantité de mouvement à paramètre négatif. La quatrième contribution fournit une étude empirique du comportement pratique des réseaux génératifs antagonistes. Dans les deuxième et troisième contributions, nous diagnostiquons que la méthode du gradient échoue lorsque le champ de vecteur du jeu est fortement rotatif. Cependant, une telle situation peut décrire un pire des cas qui ne se produit pas dans la pratique. Nous fournissons de nouveaux outils de visualisation afin d’évaluer si nous pouvons détecter des rotations dans comportement pratique des réseaux génératifs antagonistes. / Among all the historical board games played by humans, the game of go was considered one of the most difficult to master by a computer program [Van Den Heriket al., 2002]; Until it was not [Silver et al., 2016]. This odds-breaking break-through [Müller, 2002, Van Den Herik et al., 2002] came from a sophisticated combination of Monte Carlo tree search and machine learning techniques to evaluate positions, shedding light upon the high potential of machine learning to solve games. Adversarial training, a special case of multiobjective optimization, is an increasingly useful tool in machine learning. For example, two-player zero-sum games are important for generative modeling (GANs) [Goodfellow et al., 2014] and mastering games like Go or Poker via self-play [Silver et al., 2017, Brown and Sandholm,2017]. A classic result in Game Theory states that convex-concave games always have an equilibrium [Neumann, 1928]. Surprisingly, machine learning practitioners successfully train a single pair of neural networks whose objective is a nonconvex-nonconcave minimax problem while for such a payoff function, the existence of a Nash equilibrium is not guaranteed in general. This work is an attempt to put learning in games on a firm theoretical foundation. The first contribution explores minimax theorems for a particular class of nonconvex-nonconcave games that encompasses generative adversarial networks. The proposed result is an approximate minimax theorem for two-player zero-sum games played with neural networks, including WGAN, StarCrat II, and Blotto game. Our findings rely on the fact that despite being nonconcave-nonconvex with respect to the neural networks parameters, the payoff of these games are concave-convex with respect to the actual functions (or distributions) parametrized by these neural networks. The second and third contributions study the optimization of minimax problems, and more generally, variational inequalities in the context of machine learning. While the standard gradient descent-ascent method fails to converge to the Nash equilibrium of simple convex-concave games, there exist ways to use gradients to obtain methods that converge. We investigate several techniques such as extrapolation, averaging and negative momentum. We explore these techniques experimentally by proposing a state-of-the-art (at the time of publication) optimizer for GANs called ExtraAdam. We also prove new convergence results for Extrapolation from the past, originally proposed by Popov [1980], as well as for gradient method with negative momentum. The fourth contribution provides an empirical study of the practical landscape of GANs. In the second and third contributions, we diagnose that the gradient method breaks when the game’s vector field is highly rotational. However, such a situation may describe a worst-case that does not occur in practice. We provide new visualization tools in order to exhibit rotations in practical GAN landscapes. In this contribution, we show empirically that the training of GANs exhibits significant rotations around Local Stable Stationary Points (LSSP), and we provide empirical evidence that GAN training converges to a stable stationary point, which is a saddle point for the generator loss, not a minimum, while still achieving excellent performance.

This work concentrates on the study of mathematical models of human behaviour in dynamic games; in particular games with aspects of cooperation, implementation of a model and experimentation with the model. The game DarkElf was chosen for this project. It is a strategic, turn based game with economic and military features, where the decisions made by players are simultaneously implemented at a predetermined time.

In this thesis we consider constrained systems of equations. The focus is on local Newton-type methods for the solution of constrained systems which converge locally quadratically under mild assumptions implying neither local uniqueness of solutions nor differentiability of the equation function at solutions. The first aim of this thesis is to improve existing local convergence results of the constrained Levenberg-Marquardt method. To this end, we describe a general Newton-type algorithm. Then we prove local quadratic convergence of this general algorithm under the same four assumptions which were recently used for the local convergence analysis of the LP-Newton method. Afterwards, we show that, besides the LP-Newton method, the constrained Levenberg-Marquardt method can be regarded as a special realization of the general Newton-type algorithm and therefore enjoys the same local convergence properties. Thus, local quadratic convergence of a nonsmooth constrained Levenberg-Marquardt method is proved without requiring conditions implying the local uniqueness of solutions. As already mentioned, we use four assumptions for the local convergence analysis of the general Newton-type algorithm. The second aim of this thesis is a detailed discussion of these convergence assumptions for the case that the equation function of the constrained system is piecewise continuously differentiable. Some of the convergence assumptions seem quite technical and difficult to check. Therefore, we look for sufficient conditions which are still mild but which seem to be more familiar. We will particularly prove that the whole set of the convergence assumptions holds if some set of local error bound conditions is satisfied and in addition the feasible set of the constrained system excludes those zeros of the selection functions which are not zeros of the equation function itself, at least in a sufficiently small neighborhood of some fixed solution. We apply our results to constrained systems arising from complementarity systems, i.e., systems of equations and inequalities which contain complementarity constraints. Our new conditions are discussed for a suitable reformulation of the complementarity system as constrained system of equations by means of the minimum function. In particular, it will turn out that the whole set of the convergence assumptions is actually implied by some set of local error bound conditions. In addition, we provide a new constant rank condition implying the whole set of the convergence assumptions. Particularly, we provide adapted formulations of our new conditions for special classes of complementarity systems. We consider Karush-Kuhn-Tucker (KKT) systems arising from optimization problems, variational inequalities, or generalized Nash equilibrium problems (GNEPs) and Fritz-John (FJ) systems arising from GNEPs. Thus, we obtain for each problem class conditions which guarantee local quadratic convergence of the general Newton-type algorithm and its special realizations to a solution of the particular problem. Moreover, we prove for FJ systems of GNEPs that generically some full row rank condition is satisfied at any solution of the FJ system of a GNEP. The latter condition implies the whole set of the convergence assumptions if the functions which characterize the GNEP are sufficiently smooth. Finally, we describe an idea for a possible globalization of our Newton-type methods, at least for the case that the constrained system arises from a certain smooth reformulation of the KKT system of a GNEP. More precisely, a hybrid method is presented whose local part is the LP-Newton method. The hybrid method turns out to be, under appropriate conditions, both globally and locally quadratically convergent.

Motivés par la demande croissante de services de santé améliorés et à distance, qui tend à augmenter notamment avec une population de plus en plus âgée, et la réduction du coût de l'utilisation des infrastructures réseaux, afin d'assurer des applications de santé temps-réel et à faible débit de données, les réseaux de capteurs médicaux sans fil (WBANs) forment encore un domaine de recherche en forte croissance, notamment avec le développement de WBANs coopératifs. Dans ce contexte, en utilisant les utilisateurs du réseau eux-mêmes en tant que relais on pourrait étendre les infrastructures réseaux existantes, tout en améliorant la capacité du réseau et optimisant l'utilisation du spectre radio. Ainsi, les opérateurs réseaux, qui planifient déjà pour l'intégration de l'internet des objets (IoT) et l'informatique en nuage (cloud), devraient aussi penser à créer un nouveau type de réseau ad hoc mobile, où les utilisateurs du réseau sont utilisés comme des stations de base ad hoc simplifiées, afin de partager l'information en temps-réel entre des personnes colocalisées portant des capteurs corporels. Ce nouveau type de réseau est appelé réseau corporel sans fil (BBN: Body-to-Body Network). Dans un BBN, un appareil radio, collecte les données des nœuds capteurs attachés ou portés par une personne, et les transmet à un appareil récepteur situé sur une autre personne du voisinage, afin d'être traitées ou retransmises à d'autres utilisateurs du BBN. le BBN peut trouver des applications dans divers domaines tels que la santé, les sports d'équipe, le militaire, les divertissements, ainsi que des expériences passionnantes des réseaux sociaux. Fonctionnant dans la bande Industrielle, Scientifique et Médicale (ISM), les liaisons de communication dans un BBN seront très sensibles aux interférences entre les différentes technologies qui partagent le spectre radio limité. Ainsi, l'interférence entre ces technologies devient une préoccupation importante pour la conception de protocoles pour l'utilisateur final du BBN. À ce jour, très peu d'études existent, qui effectuent une analyse en profondeur de ce type de scénario implicant le corps humain dans des communications radio. Le problème d'interférence dans un tel système distribué, doit être abordé avec des mécanismes distribués, tels que la théorie des jeux. Les décideurs dans le jeu sont soit les WBANs formant le BBN ou les opérateurs de réseaux qui contrôlent les dispositifs de communication inter-WBAN. Ces dispositifs doivent faire face à des ressources de transmission limitées (bande ISM) ce qui donne lieu à des conflits d'intérêts. Cette thèse vise à explorer les opportunités pour permettre des communications inter-WBANs en assurant le partage du spectre radio par le biais de deux approches. D'abord, l'atténuation des interférences mutuelles et croisées, et par la conception d'un protocole de routage spécifique BBN utilisé dans une application de contrôle de l'expansion d'une épidémie dans les zones de rassemblement de masse, tels que les aéroports. Dans un premier volet, une approche basée sur la théorie des jeux est proposée pour résoudre le problème d'interférence distribué dans les BBNs. Le jeu d'atténuation des interférences socialement conscient des intérêts de la collectivité (SIM) a une double tâche: à l'échelle WBAN, il alloue des canaux ZigBee aux capteurs corporels pour la collecte intra-WBAN des données, et à l'échelle BBN, il alloue les canaux WiFi aux appareils mobiles pour la transmission et le relais des données inter-WBANs. Deux algorithmes, BR-SIM et SORT-SIM, ont été développés pour rechercher les points d'équilibre de Nash du jeu SIM. Le premier (BR-SIM) assure les solutions de meilleure réponse (Best-response) tandis que le second (SORT-SIM) tente d'obtenir un compromis entre des solutions quasi-optimales et un temps de convergence réduit. (...) / Motivated by the rising demand for remote and improved healthcare, while decreasing the cost of using network infrastructures to ensure time and data rate-constrained applications, Wireless Body Area Networks (WBANs) still form a strongly growing research field. Besides, engineers and researchers are investigating new solutions to supplement mobile communications through developing opportunities for cooperative WBANs. In this context, using network users themselves as relays could complement and extend existing infrastructure networks, while improving network capacity and promoting radio spectrum usage. Yet, network operators, that are already planning for the Internet of Things (IoT) and cloud computing technologies integration, should also think about this new possibility of creating a new type of mobile ad hoc network, where network users themselves are used as simplified ad hoc base stations, to fulfill the desire of sharing real-time information between colocated persons carrying body sensors. This emerging type of network is called Body-to-Body Network (BBN). In a BBN, a radio device situated on one person gathers the sensor data from the sensor nodes worn by that person, and transmit them to a transceiver situated on another person in the nearby area, in order to be processed or relayed to other BBN users. BBNs can find applications in a range of areas such as healthcare, team sports, military, entertainment, as well as exciting social networking experiences. Operating in the popular Industrial, Scientific and Medical (ISM) band, the communication links in a BBN will be heavily susceptible to interference between the different radio technologies sharing the limited radio spectrum. Thus, inter-body interference become an important concern for protocol design and quality of service for the BBN end user. Yet, higher layer MAC and networking mechanisms need to be in place to overcome this interference problem. To date, very few studies, that perform in-depth analysis of this type of body-centric scenario, exist. The interference problem in such distributed system, should be tackeled with distributed mechanisms, such as Game Theory. The decision makers in the game are either the WBANs/people forming the BBN or the network operators who control the inter-WBAN communicating devices. These devices have to cope with a limited transmission resource (ISM band) that gives rise to a conflict of interests. This thesis aims at exploring the opportunities to enable inter-WBAN communications by ensuring feasible sharing of the radio spectrum through two challenging research issues. First, mutual and cross-technology interference mitigation, and second, the design of a BBN specific routing protocol applied to an epidemic control application within mass gathering areas, such as the airport, as use case in this thesis. In a first phase, a game theoretical approach is proposed to resolve the distributed interference problem in BBNs. The Socially-aware Interference Mitigation (SIM) game performs twofold: at the WBAN stage, it allocates ZigBee channels to body sensors for intra-WBAN data sensing, and at the BBN stage, it allocates WiFi channels to mobile devices for inter-WBAN data transmitting and relaying. Two algorithms, BR-SIM and SORT-SIM, were developed to search for Nash equilibra to the SIM game. The first (BR-SIM) ensures best response solutions while the second (SORT-SIM) attempts to achieve tradeoff between sub-optimal solutions and short convergence time. Then, in order to highlight the social role of BBNs, the second part of this thesis is devoted to propose an epidemic control application tailored to BBNs, in indoor environment. This application implements a geographic routing protocol, that differentiates WBANs traffic and ensures real-time quarantine strategies. (...)

L’apprentissage automatique repose pour un bon nombre de problèmes sur la minimisation d’une fonction de coût, pour ce faire il tire parti de la vaste littérature sur l’optimisation qui fournit des algorithmes et des garanties de convergences pour ce type de problèmes. Cependant récemment plusieurs modèles d’apprentissage automatique qui ne peuvent pas être formulé comme la minimisation d’un coût unique ont été propose, à la place ils nécessitent de définir un jeu entre plusieurs joueurs qui ont chaque leur propre objectif. Un de ces modèles sont les réseaux antagonistes génératifs (GANs). Ce modèle génératif formule un jeu entre deux réseaux de neurones, un générateur et un discriminateur, en essayant de tromper le discriminateur qui essaye de distinguer les vraies images des fausses, le générateur et le discriminateur s’améliore résultant en un équilibre de Nash, ou les images produites par le générateur sont indistinguable des vraies images. Malgré leur succès les GANs restent difficiles à entrainer à cause de la nature antagoniste du jeu, nécessitant de choisir les bons hyperparamètres et résultant souvent en une dynamique d’entrainement instable. Plusieurs techniques de régularisations ont été propose afin de stabiliser l’entrainement, dans cette thèse nous abordons ces instabilités sous l’angle d’un problème d’optimisation. Nous commençons par combler le fossé entre la littérature d’optimisation et les GANs, pour ce faire nous formulons GANs comme un problème d’inéquation variationnelle, et proposons de la littérature sur le sujet pour proposer des algorithmes qui convergent plus rapidement. Afin de mieux comprendre quels sont les défis de l’optimisation des jeux, nous proposons plusieurs outils afin d’analyser le paysage d’optimisation des GANs. En utilisant ces outils, nous montrons que des composantes rotationnelles sont présentes dans le voisinage des équilibres, nous observons également que les GANs convergent rarement vers un équilibre de Nash mais converge plutôt vers des équilibres stables locaux (LSSP). Inspirer par le succès des GANs nous proposons pour finir, une nouvelle famille de jeux que nous appelons adversarial example games qui consiste à entrainer simultanément un générateur et un critique, le générateur cherchant à perturber les exemples afin d’induire en erreur le critique, le critique cherchant à être robuste aux perturbations. Nous montrons qu’à l’équilibre de ce jeu, le générateur est capable de générer des perturbations qui transfèrent à toute une famille de modèles. / Many machine learning (ML) problems can be formulated as minimization problems, with a large optimization literature that provides algorithms and guarantees to solve this type of problems. However, recently some ML problems have been proposed that cannot be formulated as minimization problems but instead require to define a game between several players where each player has a different objective. A successful application of such games in ML are generative adversarial networks (GANs), where generative modeling is formulated as a game between a generator and a discriminator, where the goal of the generator is to fool the discriminator, while the discriminator tries to distinguish between fake and real samples. However due to the adversarial nature of the game, GANs are notoriously hard to train, requiring careful fine-tuning of the hyper-parameters and leading to unstable training. While regularization techniques have been proposed to stabilize training, we propose in this thesis to look at these instabilities from an optimization perspective. We start by bridging the gap between the machine learning and optimization literature by casting GANs as an instance of the Variational Inequality Problem (VIP), and leverage the large literature on VIP to derive more efficient and stable algorithms to train GANs. To better understand what are the challenges of training GANs, we then propose tools to study the optimization landscape of GANs. Using these tools we show that GANs do suffer from rotation around their equilibrium, and that they do not converge to Nash-Equilibria. Finally inspired by the success of GANs to generate images, we propose a new type of games called Adversarial Example Games that are able to generate adversarial examples that transfer across different models and architectures.

We have examinined the problem of constructing efficient strategies for continuous-time dynamic asset allocation. In order to obtain efficient investment strategies; a stochastic optimal control approach was applied to find optimal transaction control. Two mathematical problems are formulized and studied: Model I; a dynamic programming approach that maximizes an isoelastic functional with respect to given underlying portfolio dynamics and Model II; a more sophisticated approach where a time-inconsistent state dependent mean-variance functional is considered. In contrast to the optimal controls for Model I, which are obtained by solving the Hamilton-Jacobi-Bellman (HJB) partial differential equation; the efficient strategies for Model II are constructed by attaining subgame perfect Nash equilibrium controls that satisfy the extended HJB equation, introduced by Björk et al. in [1]. Furthermore; comprehensive execution algorithms where designed with help from the generated results and several simulations are performed. The results reveal that optimality is obtained for Model I by holding a fix portfolio balance throughout the whole investment period and Model II suggests a continuous liquidation of the risky holdings as time evolves. A clear advantage of using Model II is concluded as it is far more efficient and actually takes time-inconsistency into consideration. / Vi har undersökt problemet som uppstår vid konstruktion av effektiva strategier för tidskontinuerlig dynamisk tillgångsallokering. Tillvägagångsättet för konstruktionen av strategierna har baserats på stokastisk optimal styrteori där optimal transaktionsstyrning beräknas. Två matematiska problem formulerades och betraktades: Modell I, en metod där dynamisk programmering används för att maximera en isoelastisk funktional med avseende på given underliggande portföljdynamik. Modell II, en mer sofistikerad metod som tar i beaktning en tidsinkonsistent och tillståndsberoende avvägning mellan förväntad avkastning och varians. Till skillnad från de optimala styrvariablerna för Modell I som satisfierar Hamilton-Jacobi-Bellmans (HJB) partiella differentialekvation, konstrueras de effektiva strategierna för Modell II genom att erhålla subgame perfekt Nashjämvikt. Dessa satisfierar den utökade HJB ekvationen som introduceras av Björk et al. i [1]. Vidare har övergripande exekveringsalgoritmer skapats med hjälp av resultaten och ett flertal simuleringar har producerats. Resultaten avslöjar att optimalitet för Modell I erhålls genom att hålla en fix portföljbalans mellan de riskfria och riskfyllda tillgångarna, genom hela investeringsperioden. Medan för Modell II föreslås en kontinuerlig likvidering av de riskfyllda tillgångarna i takt med, men inte proportionerligt mot, tidens gång. Slutsatsen är att det finns en tydlig fördel med användandet av Modell II eftersom att resultaten påvisar en påtagligt högre grad av effektivitet samt att modellen faktiskt tar hänsyn till tidsinkonsistens.

A presente tese evidencia o estado da arte da Teoria Jogos nas Relações Internacionais, e analisa estratégias de negociação decorrentes de processos decisórios no âmbito comercial. Ao delimitar - em tempo e espaço - a trajetória da Governança Mercantil Global, confere-se posição de destaque à Convenção de Viena de 1980 (CISG), regime dotado de ampla legitimidade, concebido sob a égide das Nações Unidas e recém ratificado pelo Brasil. A análise do referido processo de vinculação dá-se a partir de instrumentos metodológicos conferidos pela Teoria dos Jogos, culminado com a apresentação dos limites do modelo e de alternativas viáveis para seu desenvolvimento. / The present thesis sheds light on contemporary game theoretical approaches in International Relations, in particular as they pertain to the role of strategy setting in cross-border trade. The study of Global Trade Governance leads to questions of regime legitimacy, culminating with the adoption of the 1980 United Nations Vienna Convention on Contracts for the International Sale of Goods (CISG), recently ratified by Brazil. The analysis of the aforementioned ratification process validates the threshold of game theory as its stands today, and proposes, on the other hand, viable alternatives for the development of the model.

A presente tese evidencia o estado da arte da Teoria Jogos nas Relações Internacionais, e analisa estratégias de negociação decorrentes de processos decisórios no âmbito comercial. Ao delimitar - em tempo e espaço - a trajetória da Governança Mercantil Global, confere-se posição de destaque à Convenção de Viena de 1980 (CISG), regime dotado de ampla legitimidade, concebido sob a égide das Nações Unidas e recém ratificado pelo Brasil. A análise do referido processo de vinculação dá-se a partir de instrumentos metodológicos conferidos pela Teoria dos Jogos, culminado com a apresentação dos limites do modelo e de alternativas viáveis para seu desenvolvimento. / The present thesis sheds light on contemporary game theoretical approaches in International Relations, in particular as they pertain to the role of strategy setting in cross-border trade. The study of Global Trade Governance leads to questions of regime legitimacy, culminating with the adoption of the 1980 United Nations Vienna Convention on Contracts for the International Sale of Goods (CISG), recently ratified by Brazil. The analysis of the aforementioned ratification process validates the threshold of game theory as its stands today, and proposes, on the other hand, viable alternatives for the development of the model.

[pt] Esse trabalho tem como objetivo reunir os teoremas topológicos de ponto fixo clássicos e seus corolários, além de teoremas de ponto fixo provenientes da teoria do grau e algumas importantes aplicações desses teoremas a variadas áreas - desde as clássicas aplicações à teoria de EDOs e EDPs à uma aplicação à teoria dos jogos. Um exemplo é o Teorema do Ponto Fixo de Schauder-Tychonoff, para aplicações compactas em convexos de espaços localmente convexos, do qual segue como corolário que todo compacto convexo de um espaço vetorial normado (não necessariamente de dimensão finita) possui a propriedade do ponto fixo. No que se refere à teoria dos jogos em particular, foi deduzido o Teorema de Nash, que determina condições sobre as quais certos jogos possuem equilíbrios nos seus espaços das estratégias. Toda a topologia geral necessária nas demonstrações foi desenvolvida extensiva e detalhadamente a partir de topologia elementar, seguindo algumas das referências bibliográficas. O Teorema de Extensão de Dugundji - uma extensão do Teorema de Extensão de Tietze a fechados de espaços métricos sobre espaços localmente convexos -, por exemplo, é demonstrado com detalhes e usado diversas vezes ao longo da dissertação. / [en] The goal of the present work is to gather the classical fixed-point theorems and their corollaries, as well as other fixed-point theorems arising from degree theory, and some important applications to diverse fields - from the classical applications to ODEs and PDEs to an application to the game theory. An example is the Schauder-Tychonoff Fixed-Point Theorem, 1 concerning compact mappings in convex subsets of locally convex spaces, from which it follows as a corollary that every compact convex subset of a normed vector space is a fixed-point space. In regard to game theory in particular, we obtained Nash s theorem, 2 which ascertains conditions over which certain games have equilibria in their strategy spaces. All general topology necessary in the proofs was developed extensively and in details from a basic topology starting point, following some of the bibliographic references. Dugundji s Extension Theorem 3 - an extension of Tietze s Extension Theorem 4 for closed subsets of metric spaces into locally convex spaces-, for instance, is obtained with detais and used throughout the dissertation.