In this thesis we study smoothness properties of primal and dual gap functions for generalized Nash equilibrium problems (GNEPs) and finite-dimensional quasi-variational inequalities (QVIs). These gap functions are optimal value functions of primal and dual reformulations of a corresponding GNEP or QVI as a constrained or unconstrained optimization problem. Depending on the problem type, the primal reformulation uses regularized Nikaido-Isoda or regularized gap function approaches. For player convex GNEPs and QVIs of the so-called generalized `moving set' type the respective primal gap functions are continuously differentiable. In general, however, these primal gap functions are nonsmooth for both problems. Hence, we investigate their continuity and differentiability properties under suitable assumptions. Here, our main result states that, apart from special cases, all locally minimal points of the primal reformulations are points of differentiability of the corresponding primal gap function. Furthermore, we develop dual gap functions for a class of GNEPs and QVIs and ensuing unconstrained optimization reformulations of these problems based on an idea by Dietrich (``A smooth dual gap function solution to a class of quasivariational inequalities'', Journal of Mathematical Analysis and Applications 235, 1999, pp. 380--393). For this purpose we rewrite the primal gap functions as a difference of two strongly convex functions and employ the Toland-Singer duality theory. The resulting dual gap functions are continuously differentiable and, under suitable assumptions, have piecewise smooth gradients. Our theoretical analysis is complemented by numerical experiments. The solution methods employed make use of the first-order information established by the aforementioned theoretical investigations. / In dieser Dissertation wurden die Glattheitseigenschaften von primalen und dualen Gap-Funktionen für verallgemeinerte Nash-Gleichgewichtsprobleme (GNEPs) und Quasi-Variationsungleichungen (QVIs) untersucht. Diese Gap-Funktionen sind Optimalwertfunktionen von primalen und dualen Umformulierungen eines GNEPs oder QVIs als restringiertes oder unrestringiertes Optimierungsproblem. Für gewisse Teilklassen von GNEPs (Spezialfall von `player convex' GNEPs) und QVIs (`generalized moving set case') sind diese primalen Gap-Funktionen überall stetig differenzierbar, für allgemeine GNEPs und QVIs jedoch nicht. Weitere Untersuchungen der Stetigkeit und Differenzierbarkeit ergaben, dass die primalen Gap-Funktionen unter geeigneten Bedingungen, abgesehen von Sonderfällen, in allen lokalen Minima der entsprechenden primalen Umformulierung differenzierbar sind. In dieser Dissertation wurden außerdem duale Gap-Funktionen für bestimmte Klassen von GNEPs und QVIs entwickelt, indem die primalen Gap-Funktionen basierend auf einer Idee von Dietrich (H. Dietrich: A smooth dual gap function solution to a class of quasivariational inequalities. Journal of Mathematical Analysis and Applications 235, 1999, pp. 380--393) als Differenz zweier gleichmäßig konvexer Funktionen dargestellt wurden und auf diese beiden Funktionen die Toland-Singer-Dualitätstheorie angewendet wurde. Es stellte sich heraus, dass diese dualen Gap-Funktionen stetig differenzierbar sind und unter geeigneten Bedingungen sogar stückweise stetig differenzierbare Gradienten besitzen. Die Ergebnisse in dieser Dissertation wurden durch numerische Berechnungen für diverse Testprobleme mittels bekannter Optimierungsverfahren erster Ordnung unterstützt.

This thesis is concerned with a class of general-purpose algorithms for constrained minimization problems, variational inequalities, and quasi-variational inequalities in Banach spaces. A substantial amount of background material from Banach space theory, convex analysis, variational analysis, and optimization theory is presented, including some results which are refinements of those existing in the literature. This basis is used to formulate an augmented Lagrangian algorithm with multiplier safeguarding for the solution of constrained optimization problems in Banach spaces. The method is analyzed in terms of local and global convergence, and many popular problem classes such as nonlinear programming, semidefinite programming, and function space optimization are shown to be included as special cases of the general setting. The algorithmic framework is then extended to variational and quasi-variational inequalities, which include, by extension, Nash and generalized Nash equilibrium problems. For these problem classes, the convergence is analyzed in detail. The thesis then presents a rich collection of application examples for all problem classes, including implementation details and numerical results. / Die vorliegende Arbeit handelt von einer Klasse allgemein anwendbarer Verfahren zur Lösung restringierter Optimierungsprobleme, Variations- und Quasi-Variationsungleichungen in Banach-Räumen. Zur Vorbereitung wird eine erhebliche Menge an Grundmaterial präsentiert. Dies beinhaltet die Theorie von Banach-Räumen, konvexe und variationelle Analysis sowie Optimierungstheorie. Manche der angegebenen Resultate sind hierbei Verfeinerungen der entsprechenden Ergebnisse aus der Literatur. Im Anschluss wird ein Augmented-Lagrange-Verfahren für restingierte Optimierungsprobleme in Banach-Räumen präsentiert. Der Algorithmus wird hinsichtlich lokaler und globaler Konvergenz untersucht, und viele typische Problemklassen wie nichtlineare Programme, semidefinite Programme oder Optimierungsprobleme in Funktionenräumen werden als Spezialfälle aufgezeigt. Der Algorithmus wird dann auf Variations- und Quasi-Variationsungleichungen verallgemeinert, wodurch implizit auch (verallgemeinerte) Nash-Gleichgewichtsprobleme abgehandelt werden. Für diese Problemklassen werden eigene Konvergenzanalysen betrieben. Die Dissertation beinhaltet zudem eine umfangreiche Sammlung von Anwendungsbeispielen und zugehörigen numerischen Ergebnissen.

Reverse production systems are often comprised of several tiers with independent members competing at each tier. This research develops and designs a decision-making process for decentralized reverse production systems where each participant in the network determines its decisions in a self-interested way. This dissertation includes three major parts. The first part develops a prototype model for a decentralized reverse production system with two tiers, collectors and processors, focusing on the coordination of transactions of recycled items between these two tiers. The collectors determine the individual material flow allocation mechanisms, based on predictions of the range of prices from the processors, that relate the flow amount to the overall vector of acquisition prices that will be offered by the processors to all the collectors. The processors compete for the flow from the collectors and reach an equilibrium state where no entity is willing to change its decisions. In the second part, we extend the prototype model for a general multi-tiered recycling network comprised of the upstream boundary tier, several intermediate tiers, and the downstream boundary tier where each of the tiers has multiple independent entities. Recycled items flow from the top tier to the downstream tier, but acquisition prices are set from the downstream tier back to the upstream tier. Finally the third part provides a comparison of centralized and decentralized models for reverse production systems and addresses several numerical insights of different system subsidy schemes.

Peer-to-peer (p2p) approaches are an increasingly effective way to deploy services. Popular examples include BitTorrent, Skype, and KaZaA. These approaches are attractive because they can be highly fault-tolerant, scalable, adaptive, and less expensive than a more centralized solution. Cooperation lies at the heart of these strengths. Yet, in settings where working together is crucial, a natural question is: "What if users stop cooperating?" After all, cooperative services are typically deployed over multiple administrative domains, and thus vulnerable to Byzantine failures and users who may act selfishly. This dissertation explores how to construct p2p systems to tolerate Byzantine participants while also incentivizing selfish participants to contribute resources. We describe how to balance obedience against choice in building a robust p2p live streaming system. Imposing obedience is desirable as it leaves little room for peers to attack or cheat the system. However, providing choice is also attractive as it allows us to engineer flexible and efficient solutions. We first focus on obedience by using Nash equilibria to drive the design of BAR Gossip, the first gossip protocol that is resilient to Byzantine and selfish nodes. BAR Gossip relies on verifiable pseudo-random partner selection to eliminate non-determinism, which can be used to game the system, while maintaining the robustness and rapid convergence of traditional gossip. A novel fair enough exchange primitive entices cooperation among selfish peers on short timescales, thereby avoiding the need for distributed reputation schemes. We next focus on tempering obedience with choice by using approximate equilibria to guide the construction of a novel p2p live streaming system. These equilibria allow us to design incentives to limit selfish behavior rigorously, yet provide sufficient flexibility to build practical systems. We show the advantages of using an [element of]-Nash equilibrium, instead of an exact Nash, to design and implement FlightPath, our live streaming system that uses bandwidth efficiently, absorbs flash crowds, adapts to sudden peer departures, handles churn, and tolerates malicious activity. / text

Correct dosing in pharmacotherapeutics is based on the idea that too much of a drug will cause toxicity, while too little will result in failure to elicit the desired response. A major factor in the ability of a patient to handle any dose of a drug is the capacity to metabolize and eliminate that drug from the body. For the vast majority of drugs, the liver plays a key role in determining the rate at which drugs are eliminated. First, drugs must be taken up across the cell membrane into hepatocytes by uptake transporters. Once inside the hepatocyte, biotransformation enzymes metabolize and conjugate the drug to a more water-soluble compound, the distribution of which is more easily controlled. These water-soluble metabolites are then transported out of the hepatocyte by additional drug transporters either into bile for elimination, or back into the blood.More than 2 million severe adverse drug reactions occur in the US each year and often result from interindividual variation in the ability to metabolize and eliminate drugs. This number does not include medical errors, but rather circumstances where an individual is unable to handle the standard dose of the correctly prescribed drug. Although genetics plays an important role, the greatest source of variation comes from other environmental factors such as disease states. Nonalcoholic fatty liver disease (NAFLD) is a chronic condition that comprises a spectrum of histopathologies that range from simple steatosis to the more severe steatohepatitis. Specifically, nonalcoholic steatohepatitis (NASH) has become one of the leading causes for liver transplantation in the United States, and thus clearly become a considerable burden to the U.S. healthcare system.It is not known whether the capacity of the liver to metabolize and excrete drugs is altered in patients with NASH. Because the liver plays such a critical role in drug metabolism and disposition, any disease state that disrupts or modifies these functions will alter the fate of a given drug within the body. It is therefore very likely that the ability of the liver to metabolize and excrete clinically relevant drugs is compromised in NASH patients.

This qualitative case study explored the philosophy of servant-leadership in the context of sport, specifically from the perspective of an athletic leader, or servant-athlete. The primary purpose of the research was to identify traits of a servant-athlete—who for the purpose of this case study was Canadian professional basketball player Steve Nash—with the secondary purpose being to look at some formative childhood experiences, which may have shaped the servant-athlete’s leadership style. The primary method of data collection was an academic interview, with other sources of media being used to triangulate the findings. Findings suggested that the servant-athlete would be a team player, who leads by building relationships, practicing compassion, empathy, and self-awareness, and ultimately serving the needs of his teammates. It was found that childhood experiences with service—particularly related to the parents—played a large role in influencing the servant-athlete’s leadership philosophy. Rich commentary from the academic interview spoke to the themes identified, and provided evidence of servant-leadership being a viable leadership philosophy in sport. / Graduate / 0515 / 0534 / 0575 / 0384 / airritch@hotmail.com

Zugl.: Oldenburg, Universiẗat, Diss., 2007.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Habilitationsschrift--Frankfurt am Main. / Bibliography: p. 251-257.

A teoria da evolução de Darwin - como introduzida em teoria de jogos por Maynard Smith - não é o único aspecto evolucionário importante a ser considerado em uma dinâmica evolucionária, uma vez que as complexas interdependências, competição, e o crescimento podem ser modelados por, por exemplo, aspectos reativos. No jogo do ultimato, a reciprocidade e a partição meio-a-meio parecem ser um desvio do comportamento racional dos jogadores sob a luz do Equilíbrio de Nash. Tal equilíbrio emerge, por exemplo, da punição do respondedor que geralmente tende a refutar propostas injustas. Na versão iterada do jogo do ultimato, os proponentes são capazes de melhorar suas propostas por adicionar um valor a elas tornando-as mais justas. Tais aspectos evolucionários não são propriamente Darwinianos, mas eles são dotados de um aspecto fundamental: eles retêm suas ações de acordo com suas ofertas. Recentemente, uma versão reativa do jogo do ultimato onde a aceitação ocorre com probabilidade fixa foi proposta. Na primeira parte desta tese, exploramos esta versão reativa do jogo do ultimato onde a aceitação pelos jogadores depende da oferta. A fim de realizar tal procedimento, analisamos duas situações: (i) campo médio e (ii) consideramos jogadores inseridos em redes com coordenação arbitrária. Assim, mostramos então que o aspecto reativo aqui estudado, não amplamente estudado, de acordo com o nosso conhecimento, na teoria evolucionária de jogos da literatura pode desvendar um aspecto essencial para a convergência da divisão fifty-fifty. Além disso, nós também analisamos populações sobre quatro diferentes politicas que variavam de uma altamente conservadora até uma moderada, com respeito a decisão de mudar as propostas baseadas na quantidade de aceitações recebidas. Mostramos que a ideia de ganhar menos, mais vezes, adicionada a reciprocidade dos jogadores, concomitantemente ao lema do \dando mais pra receber mais" , é altamente relevante para o conceito de populações economicamente saudáveis que barganham. Finalmente, para completar nossos estudos no jogo do ultimato reativo, adicionamos a mobilidade aos jogadores. Neste caso, realizamos algumas mudanças levando em consideração então a seleção natural (cópia Darwiniana). Mostramos que a mobilidade lidera a menores ofertas médias e também elaboramos um estudo complementar que mostra os valores médios das densidades de ofertas e estratégias/politicas mediadas em intervalos finais para grandes tempos de evolução temporal. Nossos resultados sugerem que apesar de uma coexistência temporária, a política/estratégia III (só oferece menos se todos aceitarem) deve prevalecer em relação a todas as outras em redes quadradas considerando apenas 4 vizinhos sob os efeitos de mobilidade. Finalmente, na segunda parte desta tese, continuamos a estudar os efeitos de mobilidade, no entanto, em outro paradigma da teoria de jogos, mais precisamente no que tange aos dilemas sociais relacionados aos conitos entre cooperação e interesses próprios de indivíduos em grandes populações, uma vez que a emergência da cooperação e sua manutenção é a chave para o entendimento dos conceitos fundamentais sobre a evolução das espécies. A fim de entender os mecanismos envolvidos neste contexto, aqui estudamos o jogo de bem público opcional com foco nos efeitos dos aspectos difusivos nos padrões emergentes de dominância cíclica entre as diferentes estratégias. Diferentemente de outros trabalhos, mostramos que os padrões de pedra-papel-tesoura (RPS, em inglês, rock-paper-scissors) ocorrem por introduzir no jogo um tipo simples de mobilidade aleatória em uma rede esparsadamente ocupada. Tal padrão tem se revelado muito importante na conservação das espécies em ambientes ecológicos e sociais. Uma das mais importantes contribuições desta tese é mostrar que não precisamos de esquemas mais elaborados para construção da vizinhança no jogo para observar padrões de RPS como sugerido na literatura. Como um interessante resultado adicional, propomos um método alternativo para quantificar a densidade de RPS em um contexto quantitativo da teoria de jogos que torna possível realizar um estudo de tamanho finito. Tal abordagem pode ser muito interessante para ser aplicada em outros jogos genericamente. / Darwin's theory of evolution - as introduced in game theory by Maynard Smith - is not the only important evolutionary aspect in evolutionary dynamics, since complex interdependencies, competition, and growth should be modeled by, for example, reactive aspects. In the ultimatum game, the reciprocity and the fty- fty partition seems to be a deviation from rational behaviour of the players under the light of Nash equilibrium. Such equilibrium emerges, for example, from the punishment of the responder who generally tends to refuse unfair proposals. In the iterated version of the game, the proposers are able to improve their proposals by adding a value thus making fairer proposals. Such evolutionary aspects are not properly Darwinian-motivated, but they are endowed with a fundamental aspect: they re ect their actions according to value of the o ers. Recently, a reactive version of the ultimatum game where acceptance occurs with xed probability was proposed. In the rst part of this thesis, we aim at exploring this reactive version of the ultimatum game where the acceptance by players depends on the o er. In order to do so, we analyse two situations: (i) mean eld and (ii) we consider players inserted within the networks with arbitrary coordination. We then show that the reactive aspect, here studied, thus far not analysed in the evolutionary game theory literature can unveil an essential feature for the convergence to fty- fty split. Moreover we also analyse populations under four di erent polices ranging from a highly conservative to a moderate one, with respect to the decision in changing the proposal based on acceptances. We show that the idea of gaining less more times added to the reciprocity of the players is highly relevant to the concept of "healthy"societies population bargaining. Finally by completing our studies in the reactive ultimatum game, we added mobility to the players. In this case, we performed some changes taking into account the natural selection (Darwinian copy). We show that mobility leads to lower average o ers and we also elaborated color maps for all occupation and mobility values show the density of o ers and strategies/polices which suggests a temporary coexistence. Finally, in the second part of this thesis, we explore the mobility e ects which are very important in social dilemmas that concern a natural con ict between cooperation and self interests among individuals in large populations. The emergence of cooperation and its maintenance is the key for the understanding of fundamental concepts about the evolution of species. In order to understand the mechanisms involved in this framework, here we study the Optional Public Good Games with focus on the e ects of di usive aspects in the emergent patterns of cyclic dominance between the strategies. Di erently from other works, we showed that rock-paper-scissors (RPS) patterns occur by introducing a simple kind of random mobility in a lattice sparsely occupied. Such pattern has been revealed to be very important in the conservation of the species in ecological and social environments. The goal of this paper is to show that we do not need more elaborated schemes for construction of the neighbourhood in the game to observe RPS patterns as suggested in the literature. As an interesting additional result, in this contribution we also propose an alternative method to quantify the RPS density in a quantitative context of the game theory which becomes possible to perform a nite size scaling study. Such approach can be very interesting to be applied in other games generically.