Made available in DSpace on 2014-06-12T18:31:37Z (GMT). No. of bitstreams: 2 arquivo9588_1.pdf: 621138 bytes, checksum: bb527e33f8271d46f77af1bdea3dc7fd (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2012 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Neste trabalho tratamos da existência de orbitas periodicas numa vizinhanca de equilibrios relativos no problema de n vortices no plano e na esfera. Mais especificamente, no plano, o equilibrio relativo consiste de n vortices unitarios nos vertices de um poligono regular inscrito numa circunferência centrada na origem com e sem um vortice de intensidade no centro. Na esfera consiste de n vortices unitarios nos vertices de um poligono regular inscrito numa circunferência em uma latitude fixa da esfera com e sem um vortice de intensidade no polo norte. A ferramenta basica utilizada e o Teorema do Centro de Lyapunov

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The analysis of the computational aspects of strategic situations is a basic field in Computer Sciences. Two main topics related to strategic games have been developed. First, introduction and analysis of a class of games (so called angel/daemon games) designed to asses web applications, have been considered. Second, the problem of isomorphism between strategic games has been analysed. Both parts have been separately considered. Angel-Daemon Games A service is a computational method that is made available for general use through a wide area network. The performance of web-services may fluctuate; at times of stress the performance of some services may be degraded (in extreme cases, to the point of failure). In this thesis uncertainty profiles and Angel-Daemon games are used to analyse servicebased behaviours in situations where probabilistic reasoning may not be appropriate. In such a game, an angel player acts on a bounded number of ¿angelic¿ services in a beneficial way while a daemon player acts on a bounded number of ¿daemonic¿ services in a negative way. Examples are used to illustrate how game theory can be used to analyse service-based scenarios in a realistic way that lies between over-optimism and over-pessimism. The resilience of an orchestration to service failure has been analysed - here angels and daemons are used to model services which can fail when placed under stress. The Nash equilibria of a corresponding Angel-Daemon game may be used to assign a ¿robustness¿ value to an orchestration. Finally, the complexity of equilibria problems for Angel-Daemon games has been analysed. It turns out that Angel-Daemon games are, at the best of our knowledge, the first natural example of zero-sum succinct games. The fact that deciding the existence of a pure Nash equilibrium or a dominant strategy for a given player is Sp 2-complete has been proven. Furthermore, computing the value of an Angel-Daemon game is EXP-complete. Thus, matching the already known complexity results of the corresponding problems for the generic families of succinctly represented games with exponential number of actions. Game Isomorphism The question of whether two multi-player strategic games are equivalent and the computational complexity of deciding such a property has been addressed. Three notions of isomorphisms, strong, weak and local have been considered. Each one of these isomorphisms preserves a different structure of the game. Strong isomorphism is defined to preserve the utility functions and Nash equilibria. Weak isomorphism preserves only the player preference relations and thus pure Nash equilibria. Local isomorphism preserves preferences defined only on ¿close¿ neighbourhood of strategy profiles. The problem of the computational complexity of game isomorphism, which depends on the level of succinctness of the description of the input games but it is independent of the isomorphism to consider, has been shown. Utilities in games can be given succinctly by Turing machines, boolean circuits or boolean formulas, or explicitly by tables. Actions can be given also explicitly or succinctly. When the games are given in general form, an explicit description of actions and a succinct description of utilities have been assumed. It is has been established that the game isomorphism problem for general form games is equivalent to the circuit isomorphism when utilities are described by Turing Machines; and to the boolean formula isomorphism problem when utilities are described by formulas. When the game is given in explicit form, it is has been proven that the game isomorphism problem is equivalent to the graph isomorphism problem. Finally, an equivalence classes of small games and their graphical representation have been also examined.

[pt] Este trabalho desenvolve e estabelece a existência de equilíbrio para um modelo sequencial com dois estágios, mercados financeiros incompletos, risco de crédito e colateral endógeno. No primeiro estágio, ao escolherem o colateral, de acordo com uma regra exogenamente determinada, os agentes emitem ativos personalizados que serão transacionados no segundo estágio, em uma economia Walrasiana com dois períodos. A nossa estrutura permite o surgimento de modelos nos quais os próprios agentes escolhem suas garantias, de forma similar aos modelos já existentes de colateral endógeno. Tais modelos exibem o que podemos chamar de A Maldição do Vencedor, situação na qual o agente escolhe, racionalmente, oferecer colateral nulo, inviabilizando, em equilíbrio, a transação de ativos. Com isso, a economia é jogada para um equilíbrio Pareto inferior no qual não existem mercados financeiros. Ao introduzir uma sequencialidade nas escolhas, conseguimos resolver esse problema, pois os agentes antecipam o efeito da escolha de colateral sobre os payoffs de equilíbrio, escolhendo, racionalmente, colaterais positivos. Assim, conseguimos não somente solucionar uma limitação dos modelos existentes, como ainda, permitir o surgimento de inúmeros sub-modelos através das diversas possibilidades para a regra de escolha na determinação do colateral. / [en] This paper develops and establishes the existence of equilibrium for a sequential model with two stages, incomplete financial markets, credit risk and endogenous collateral. In the first stage, by choosing the collateral, according to a predetermined and exogenously given rule, the agents issue personalized securities that will be traded in the second stage in aWalrasian economy with two periods. Our structure allows for models in which the agents choose their own collateral, similar to the existing endogenous collateral models. Those models exhibit what we might call, The Winner s Curse, a situation in which the agent choose, rationally, to offer no collateral, making asset trading impossible, in equilibrium. The economy is then thrown in a Paretoinferior equilibria in which there are no financial markets. By introducing the agent s choice in a sequential fashion, we avoid such a problem, because the agents anticipate the effects of their collateral choice over the equilibrium payoffs, therefore choosing rationally, positive collateral. That way, we are able, not only to solve a shortcoming of the existing models, but also to allow for a variety of sub-models through the several possible choices for the collateral determining rule.

[pt] Este trabalho tem por objetivo analisar uma das formas de financiamento da República Federativa do Brasil: a venda de títulos da dívida pública. Para isso serão analisadas diversas informações oficiais dos órgãos competentes, relacionadas às regras que permeiam este tipo de negociação. Além disso, serão explorados trabalhos correlatos e suas principais contribuições. Por fim, o texto busca mostrar qual formato de leilão é, teoricamente, a mais vantajosa para o Tesouro Nacional negociar seus títulos de dívida. / [en] This work aims to analyze one of the forms of financing the Federative Republic of Brazil: the sale of government bonds. For this, varied information from official agencies related to the rules that govern this type of negotiation will be analyzed. In addition, related works and their main contributions will be explored. Finally, the text seeks to show which auction format is, theoretically, the most advantageous for the National Treasury to negotiate its debt securities.

Esta tesis consta de tres proyectos sobre coordinación y los conflictos utilizando un enfoque experimental. El capítulo 1 estudia si un mecanismo de votación incentiva una coordinación eficiente y concluye en comparación a un sistema de decisión carente de votación (regla del dictador), ambos mecanismos (decisión por mayoría y decisión unánime) son eficaces incentivando la coordinación en la toma de decisiones posteriores. El capítulo 2 se centra en los fallos de coordinación e investiga si una "mancha solar" puede causar un problema de coordinación sobre el equilibrio Pareto-Superior. De los resultados, se deduce que una señal aleatoria exógena genera ineficiencias, aunque sería simplemente mejor ignorarla. Por último, el capítulo 3 estudia un juego de concurso en una red de conflicto. Los resultados demuestran que las estructuras de red en cuestión importan en la determinación del nivel de las inversiones en tecnología de conflicto y, por lo tanto, afectan la intensidad total de los conflictos. / This thesis is a collection of three research projects on coordination and conflict using an experimental approach. Chapter 1 studies whether a voting mechanism induces efficient coordination; and, concludes that compared to a dictator rule where voting is absent, both of the voting rules studied, i.e. majority and unanimity, are successful in inducing coordination in subsequent decisions. Chapter 2 focuses on coordination failures and investigates whether a sunspot leads to failure in coordinating on the Pareto-Superior equilibrium; and in fact, deduces that a random exogenous signal leads to inefficiencies even though it would simply be better if ignored. Finally, chapter 3 studies a contest game in a conflict network. It shows that network structures matter in determining the level of individual investments in the conflict technology, and hence affect total conflict intensity.

[pt] Este trabalho analisa um mercado de eletricidade em que os geradores declaram funções de custo quadráticas para o operador da rede e também suas disponibilidades máximas de produção. O operador, então, determina as quantidades a serem produzidas por cada gerador de modo a atender a uma demanda inelástica, ao menor custo possível. Estabelecem-se alguns resultados que permitem computar os equilíbrios de Nash deste modelo e descrevem-se algumas de suas propriedades, tais como condições de existência. / [en] This work analyzes an electricity market in which generators declare quadratic cost functions for the grid operator and also the maximum capacity available. The operator then determines the quantities that each generator must produce to meet an inelastic demand at the lowest possible cost. Some results are established that allow computing the Nash equilibria of this model and some of their properties are described, such as existence conditions.