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As relações internacionais de interdependência no setor de etanol e suas implicações na cadeia de produção brasileiraFagundes, Paloma de Mattos January 2012 (has links)
A expansão do mercado global de bioenergia é tida como uma alternativa promissora para alguns países, especialmente os potenciais produtores e fornecedores de matéria-prima, como é o caso do Brasil. A inserção do etanol na matriz energética de diferentes países produtores e consumidores será um fenômeno complexo com diferentes tipos de relações de interdependência. Este trabalho visa analisar as relações internacionais de interdependência entre Brasil e outros países produtores e consumidores - reais ou potenciais - do biocombustível etanol e as suas implicações sobre a cadeia produtiva de etanol no Brasil. Para estudar esse processo de interdependência nas relações internacionais, este trabalho explora a Teoria da Interdependência Complexa proposta por Robert Keohane e Joseph Samuel Nye Junior (2001) e a Teoria dos Jogos de John Von Neumann e Oskar Morgenstern (1944). Foi realizada uma pesquisa quali-quantitativa, por meio da análise documental com a utilização do software QDA Miner® e da aplicação de dois questionários. Para a análise documental, foram usados 101 documentos classificados como atos internacionais do setor de biocombustíveis e etanol entre os anos de 2002 e 2011, presentes nas bases de dados do governo brasileiro. O primeiro questionário, respondido por 46 mestres e doutores que trabalham ou realizam pesquisas nas áreas de etanol, agronegócios e/ou relações internacionais, buscou identificar as palavras-chave que se relacionam com as dimensões políticas, econômicas, socioambientais e técnicas no setor de etanol. O segundo questionário, respondido por 21 representantes das partes interessadas da cadeia produtiva do etanol brasileiro, visou analisar, através da lógica da teoria dos jogos, o comportamento estratégico dos atores, em uma condição de interação estratégica. A análise dos resultados demonstra que os principais atores das relações de interdependência com o Brasil no setor de etanol são Estados Unidos com um grau de interdependência alto, a Europa com um grau de interdependência médio e a China com um grau de interdependência muito baixo. As dimensões com maior desempenho nas relações de interdependência, tanto do ponto de vista dos atos internacionais como das partes interessadas, foram a dimensão política, a dimensão econômica, seguida pela dimensão técnica e socioambiental. Assim, considera-se que o comportamento estratégico observado nas relações de interdependência demonstrou que nas relações entre Brasil e Estados Unidos, o Brasil tende a ganhar pouco enquanto que os Estados Unidos tende a ganhar muito. Nas relações entre Brasil e Europa, o Brasil tende a perder muito enquanto que a Europa tende a ganhar muito, e nas relações entre Brasil e China, o Brasil tende a ganhar pouco enquanto que a China não perde nem ganha. Portanto, indiferente da interdependência existente nas relações entre os atores, sejam produtores e consumidores reais ou potenciais, todos devem buscar forças para o fortalecimento do setor, uma vez que todo o sistema global estará se beneficiando, tanto no âmbito político, econômico, socioambiental ou técnico. Esforços tecnológicos para ganhos de eficiência voltados para o crescimento sustentável da produção, criação de políticas setoriais, que ofereçam segurança e infraestrutura para a sua produção, redução de tarifas que incidem sobre o produto em todo o mundo, transformação do etanol em uma commodity global com grande número de países comprando e vendendo esse produto são algumas das ações que poderão fazer com que o etanol assuma uma posição cada vez mais estratégica na diversificação da matriz energética mundial. / The expansion of the global bioenergy market is regarded as a promising alternative for some countries, especially the potential producers and suppliers of raw materials, as in the case of Brazil. The insertion of ethanol in the energy matrix from different countries producers and consumers will be a complex phenomenon with different types of interdependent relations. This paper aims to analyze the international relations of interdependence among Brazil and other countries producers and consumers – real or potential – of the ethanol biofuel and their implications on the productive chain of this fuel in Brazil. To study this process of interdependence in international relations, this work explores the Theory of Complex Interdependence proposed by Robert Keohane and Joseph Nye Samuel Junior (2001) and the Game Theory of John Von Neumann and Oskar Morgenstern (1944). It was performed a quali-quantitative, research through a documentary analysis with the use of QDA Miner ® software and the application of two questionnaires. For the document analysis, 101 classified documents were used, as international acts of biofuels and ethanol among 2002 and 2011, present in the databases of the Brazilian government. The first questionnaire, answered by 46 teachers and doctors who work or conduct research in ethanol, agribusiness and/or international relations areas, intended to identify the keywords related to the political, economic, social and environmental dimensions and techniques in the ethanol sector. The second questionnaire, answered by 21 representatives of stakeholders in the productive chain of Brazilian ethanol, aimed to analyze, through the logic of the Game Theory, the strategic behavior of actors in a condition of strategic interaction. The analysis of the results shows that the main actors of the interdependent relations with Brazil in the ethanol sector are The United States, with a high degree of interdependence, Europe with an average degree of interdependence and China with a low degree of interdependence. The dimensions with higher performance in relations of interdependence, both from the point of view of international acts as stakeholders, were the political and economic dimensions, followed by technical and socio-environmental dimensions. Thus, it is considered that the strategic behavior observed in relations of interdependence demonstrated that in relations between Brazil and United States, Brazil tends to earn a little, while the United States tends to earn a lot. Relations between Brazil and Europe show that Brazil tends to lose a lot, while Europe tends to earn a lot, and in relations between Brazil and China, Brazil tends to earn a little, while China neither lose nor earn. Therefore, regardless of existing interdependence in relations among the actors, whether real or potential producers and consumers, all the countries should work together to strengthen the industry, since the entire global system will be benefiting, both in the political, economic, social or technical sectors. Technological efforts for efficiency gains related to the sustainable growth of production, creation of sectoral policies, which offer security and infrastructure for its production, reduction of tariffs on the product in all over the world, transformation of ethanol into a global commodity with a large number of countries buying and selling this product are some of the actions that could make ethanol takes an increasingly strategic position on the diversification in the energy matrix.
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Redução do espaço de busca de estruturas de coalizão a partir de informações sobre o domínio : uma aplicação em smart grids / Reduction of coalition structures’ search space based on domain information: an application in smart gridsRamos, Gabriel de Oliveira January 2013 (has links)
Redes elétricas desempenham um papel fundamental no que tange à distribuição de energia elétrica. Entretanto, as redes elétricas convencionais são muito antigas, apresentando uma série de deficiências e inseguranças. Neste cenário surgem as redes elétricas inteligentes, mais conhecidas como smart grids. Smart grids são uma evolução para as redes elétricas tradicionais, apresentando como grande diferencial a presença intensiva de tecnologia de ponta para monitorar cada elemento que a compõe. Uma das principais características de smart grids é seu fluxo bidirecional de energia e informação, que permite a qualquer elemento tanto consumir quanto fornecer energia para a rede, seja um aerogerador ou mesmo uma residência. Tal característica vai de encontro à necessidade de se distribuir a produção energética, tornando-a mais robusta e tolerante a falhas. Uma tecnologia que surgiu em meio ao desenvolvimento de smart grids denomina-se Veículo-Para-Rede (V2G, do inglês Vehicle-To-Grid). Através de sessões V2G, veículos elétricos (EVs, em inglês electric vehicles) podem vender a energia de suas baterias para a rede, obtendo lucro com este procedimento. Existem duas vantagens nesta tecnologia. Por um lado, proprietários de EVs podem obter lucro com a venda de energia, reduzindo os custos de se manter seu veículo. Por outro lado, a rede como um todo se beneficia, pois as baterias podem ser utilizadas para aumentar a estabilidade da rede. Entretanto, para que estas vantagens sejam expressivas, é necessário utilizar-se de mecanismos para aumentar a eficiência do processo V2G, uma vez que baterias são muito caras. Uma alternativa que tem sido muito explorada é a formação de coalizões entre os EVs. A proposta deste trabalho é utilizar informações sobre o domínio de smart grids de modo a impor restrições no processo de formação de coalizões de EVs, visando à redução do espaço de busca de estruturas de coalizão. Especificamente, estabelece-se a distância máxima que pode haver entre dois EVs de uma mesma coalizão, através da qual é possível identificar e podar porções inválidas do espaço de busca. Para tanto, é proposto o algoritmo CPCSG, capaz de identificar restrições entre os EVs e de podar o espaço de busca. A abordagem proposta pode ser utilizada em conjunto com algoritmos de geração de estruturas de coalizão para torná-los mais rápidos e eficientes. Com base em experimentos, percebe-se que a abordagem proposta proporciona um ganho notável de desempenho e uma redução expressiva no uso de memória em relação a outros algoritmos para geração de estruturas de coalizão. Em geral, quanto mais restritiva a rede e quanto maior o número de agentes, maior será o percentual do espaço de busca passível de ser podado. Resultados mostram, ainda, que quando comparada com outros algoritmos de geração de estruturas de coalizão, a técnica proposta chega a superar o tempo dos demais em diversas ordens de magnitude. / Electric grids play a key role in the energy distribution process. However, conventional grids are very old, which causes the onset of weaknesses and uncertainties. In such a scenario the smart grid concept arises. Smart grids are an evolution to the ageing electric grids, whose major breakthrough is the intensive use of technology to monitor every element that comprises it. One of the main features of smart grids is its bi-directional flow of electricity and information, which allows any element to consume and even supply energy to the grid, regardless of being a wind turbine or even a residence. Such a characteristic meets the need to make the energy production more distributed, making it more robust and fault tolerant. Amidst the development of smart grids emerged the concept of Vehicle-To-Grid (V2G). Through V2G sessions, electric vehicles (EVs) can sell the surplus energy of their batteries to the grid, making a profit. Two advantages arise from this technology. First, EVs’ owners can make a profit from the sale of energy, reducing their vehicles’ maintenance cost. Second, the network as a whole is benefited as batteries could be used to increase the network stability. However, in order to benefit from such advantages, it is necessary the use mechanisms to increase the efficiency of the V2G process, since batteries are very expensive. One way that has been explored is the coalition formation among EVs. The proposal of this work is to use smart grids’ domain information to impose constraints on the coalition formation process in order to reduce the coalition structures’ search space. Specifically, we define a maximum distance that can exist between two EVs of a given coalition, through which it is possible to identify and prune invalid portions of the search space. To this end, we propose the CPCSG algorithm, which has the capability of identifying constraints among EVs and pruning the search space. The proposed approach can be used together with coalition structure generation algorithms to make them faster and more efficient. Based on experiments, it can be seen that our approach provides a noticeable performance gain and a significant memory usage reduction compared to other coalition structure generation algorithms. In general, the more restrictive the grid and the greater the number of agents, the greater the percentage of the search space that can be pruned. Results also show that when compared with other coalition structure generation algorithms, the proposed technique is able to overcome the other in time by several orders of magnitude.
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Ensaios sobre o desmatamento : corrupção, jogos diferenciais, e evidência empírica / Proposal for a model of customer profitability : a case study of company area foodMendes, Cassandro Maria da Veiga January 2011 (has links)
O presente estudo tem como objetivo analisar o fenômeno do desmatamento no Brasil. Para este efeito, utilizou-se de instrumentais econométricos e matemáticos. O estudo se divide em três ensaios. No primeiro ensaio investigam-se os possíveis efeitos adversos da política governamental devido à existência de fracas instituições na maior parte da região da Amazônia legal. Neste primeiro ensaio também é analisado empiricamente a relação entre corrupção, desmatamento e Produto Interno Bruto (PIB) para os municípios de Mato Grosso. No segundo ensaio utiliza-se de jogos diferenciais para analisar teoricamente o efeito da corrupção no nível de desmatamento ilegal. Finalmente o terceiro ensaio, focalizando numa análise regional, faz-se uma análise empírica, através de modelos não paramétricos, para a relação entre corrupção, desmatamento, e PIB. No terceiro ensaio, também, utilizando-se de modelos não paramétricos, estima-se, numa análise internacional, a existência da curva de Kuznets. / The present study aims to analyze the phenomenon of deforestation in Brazil. For this purpose, we used econometrics and mathematical tools. The study is divided into three essays. In the first essay, through the standard game theory, we investigated the adverse effects of the government policy due the existence of weak institutions in the Amazon region. In this first essay it is also studied empirically, for the municipalities of Mato-grosso, the relationship between corruption, deforestation and Gross Domestic Product (GDP). In the second essay we used differential game theory to analyze the effect of corruption on the level of illegal logging. Finally on the third essay, we focused on a regional and international analysis. For the regional analysis, we used nonparametric models to test the relationship between corruption, deforestation, and GDP. We used the same methods to perform an international analysis related with the Kuznets curve.
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Data-Driven and Game-Theoretic Approaches for PrivacyJanuary 2018 (has links)
abstract: In the past few decades, there has been a remarkable shift in the boundary between public and private information. The application of information technology and electronic communications allow service providers (businesses) to collect a large amount of data. However, this ``data collection" process can put the privacy of users at risk and also lead to user reluctance in accepting services or sharing data. This dissertation first investigates privacy sensitive consumer-retailers/service providers interactions under different scenarios, and then focuses on a unified framework for various information-theoretic privacy and privacy mechanisms that can be learned directly from data.
Existing approaches such as differential privacy or information-theoretic privacy try to quantify privacy risk but do not capture the subjective experience and heterogeneous expression of privacy-sensitivity. The first part of this dissertation introduces models to study consumer-retailer interaction problems and to better understand how retailers/service providers can balance their revenue objectives while being sensitive to user privacy concerns. This dissertation considers the following three scenarios: (i) the consumer-retailer interaction via personalized advertisements; (ii) incentive mechanisms that electrical utility providers need to offer for privacy sensitive consumers with alternative energy sources; (iii) the market viability of offering privacy guaranteed free online services. We use game-theoretic models to capture the behaviors of both consumers and retailers, and provide insights for retailers to maximize their profits when interacting with privacy sensitive consumers.
Preserving the utility of published datasets while simultaneously providing provable privacy guarantees is a well-known challenge. In the second part, a novel context-aware privacy framework called generative adversarial privacy (GAP) is introduced. Inspired by recent advancements in generative adversarial networks, GAP allows the data holder to learn the privatization mechanism directly from the data. Under GAP, finding the optimal privacy mechanism is formulated as a constrained minimax game between a privatizer and an adversary. For appropriately chosen adversarial loss functions, GAP provides privacy guarantees against strong information-theoretic adversaries. Both synthetic and real-world datasets are used to show that GAP can greatly reduce the adversary's capability of inferring private information at a small cost of distorting the data. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2018
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Definição e especificação formal do jogo diferencial Lobos e Cordeiro / Definition and formal specification of the differential game wolfs and lambSulzbach, Sirlei Ines January 2005 (has links)
No presente trabalho serão apresentadas questões usuais em jogos diferenciais, nos quais os jogadores envolvidos têm objetivos diferentes; ou seja, enquanto um dos jogadores tenta fugir, o outro tenta pegar. Além disso, será definido um modelo de especificação para o jogo diferencial lobos e cordeiro. As Redes de Petri foram escolhidas como forma de especificação para o jogo proposto. Assim, o objetivo será estabelecer estratégias eficientes para o jogo lobos e cordeiro para que se possa realizar um estudo da complexidade das questões apresentadas para este jogo, levando-se em consideração a especificação formal apresentada para tal jogo. / In this work usual questions in differential games will be presented, in which the involved players have different objectives; that is, while one of the players tries "to run away", the other tries "to catch". Moreover, a specification for the differential game "wolves and lamb" will be defined. The Petri Nets had been chosen as specification formalism for the considered game. Thus, the objective is to establish efficient strategies for the game wolves and lamb so that we can carry out a study of the complexity of the presented questions, taking into consideration the presented formal specification for the game.
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Effect of Chaos and ComplexWave Pattern Formation in Multiple Physical Systems: Relativistic Quantum Tunneling, Optical Meta-materials, and Co-evolutionary Game TheoryJanuary 2012 (has links)
abstract: What can classical chaos do to quantum systems is a fundamental issue highly relevant to a number of branches in physics. The field of quantum chaos has been active for three decades, where the focus was on non-relativistic quantumsystems described by the Schr¨odinger equation. By developing an efficient method to solve the Dirac equation in the setting where relativistic particles can tunnel between two symmetric cavities through a potential barrier, chaotic cavities are found to suppress the spread in the tunneling rate. Tunneling rate for any given energy assumes a wide range that increases with the energy for integrable classical dynamics. However, for chaotic underlying dynamics, the spread is greatly reduced. A remarkable feature, which is a consequence of Klein tunneling, arise only in relativistc quantum systems that substantial tunneling exists even for particle energy approaching zero. Similar results are found in graphene tunneling devices, implying high relevance of relativistic quantum chaos to the development of such devices. Wave propagation through random media occurs in many physical systems, where interesting phenomena such as branched, fracal-like wave patterns can arise. The generic origin of these wave structures is currently a matter of active debate. It is of fundamental interest to develop a minimal, paradigmaticmodel that can generate robust branched wave structures. In so doing, a general observation in all situations where branched structures emerge is non-Gaussian statistics of wave intensity with an algebraic tail in the probability density function. Thus, a universal algebraic wave-intensity distribution becomes the criterion for the validity of any minimal model of branched wave patterns. Coexistence of competing species in spatially extended ecosystems is key to biodiversity in nature. Understanding the dynamical mechanisms of coexistence is a fundamental problem of continuous interest not only in evolutionary biology but also in nonlinear science. A continuous model is proposed for cyclically competing species and the effect of the interplay between the interaction range and mobility on coexistence is investigated. A transition from coexistence to extinction is uncovered with a non-monotonic behavior in the coexistence probability and switches between spiral and plane-wave patterns arise. Strong mobility can either promote or hamper coexistence, while absent in lattice-based models, can be explained in terms of nonlinear partial differential equations. / Dissertation/Thesis / Ph.D. Electrical Engineering 2012
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Institutional Analysis of Water Management for Agriculture in the Chancay-Lambayeque Basin, PeruJanuary 2013 (has links)
abstract: This research presents an analysis of the main institutions and economic incentives that drive farmers behaviors on water use in the Chancay-Lambayeque basin, located in Lambayeque (Peru), a semi arid area of great agricultural importance. I focus my research on identifying the underlying causes of non-collaborative behaviors in regard to water appropriation and infrastructure provisioning decision that generates violent conflicts between users. Since there is not an agreed and concrete criteria to assess "sustainability" I used economic efficiency as my evaluative criteria because, even though this is not a sufficient condition to achieve sustainability it is a necessary one, and thus achieving economic efficiency is moving towards sustainable outcomes. Water management in the basin is far from being economic efficient which means that there is some room for improving social welfare. Previous studies of the region have successfully described the symptoms of this problem; however, they did not focus their study on identifying the causes of the problem. In this study, I describe and analyze how different rules and norms (institutions) define farmers behaviors related to water use. For this, I use the Institutional Analysis and Development framework and a dynamic game theory model to analyze how biophysical attributes, community attributes and rules of the system combined with other factors, can affect farmers actions in regard to water use and affect the sustainability of water resources. Results show that water rights are the factor that is fundamental to the problem. Then, I present an outline for policy recommendation, which includes a revision of water rights and related rules and policies that could increase the social benefits with the use of compensation mechanisms to reach economic efficiency. Results also show that commonly proposed solutions, as switch to less water intensive and more added value crops, improvement in the agronomic and entrepreneurial knowledge, or increases in water tariffs, can mitigate or exacerbate the loss of benefits that come from the poor incentives in the system; but they do not change the nature of the outcome. / Dissertation/Thesis / M.A. Sustainability 2013
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L'improvisation collective libre : de l'exigence de coordination à la recherche de points focaux. : cadre théorique. Analyses. Expérimentations. / Collective free improvisation : From coordination's requirements to the finding of focal points. : Theorical framework, analysis, experimentations.Canonne, Clément 22 November 2010 (has links)
On s'intéresse ici à une classe particulière de phénomènes musicaux improvisés : ceux qui réunissent au moins deux musiciens improvisant simultanément et librement. Les musiciens placés dans cette situation doivent affronter un problème particulier : il n'y a aucun ensemble intersubjectif de données musicales (voire extra-musicales) qui vienne contrôler non seulement le devenir formel de l'improvisation (inter-détermination horizontale) mais encore la coexistence concurrente des différents discours improvisés (inter-détermination verticale).A partir de là, il s'agit de montrer que l'on peut penser l'improvisation collective libre, en tant qu'elle est une situation interactive, stratégique et collaborative, sous la catégorie générique du problème de coordination.Cette appartenance étant posée, la question est ensuite envisagée sous différents angles. Dans la première partie, la théorie des jeux, en particulier la théorie des points focaux, est mobilisée pour déterminer les heuristiques cognitives qui seront utilisées par les improvisateurs pour parvenir effectivement à se coordonner. On montre dans la deuxième partie la place centrale qu'occupe l'idée de coordination dans la dynamique et la gestion formelle d'une improvisation collective libre. Le cadre théorique est finalement confronté à deux types de données empiriques : des analyses d'extraits du festival Company Week, organisé par le guitariste Derek Bailey, dans la troisième partie ; et les résultats de cinq proto-expérimentations menées auprès de musiciens issus de la Norwegian Academy of Music et du CNSMD de Lyon, dans la quatrième partie. / This thesis deals with a specific class of musically improvised phenomenons : the one's that are produced by at least two musicians in simultaneous and open improvisation. Musicians in this situation face a specific challenge : the lack of common mmusical (or non-musical) set of imputs which can shape the formal process of the improvisation (horizontal indeterminacy) or assure the mutual coexistence of the improvised discourses (vertical indeterminacy).In the following, we postulate that collective free improvisation, as an interactive, strategic and collaborative situation, falls under the generic category of coordination problems.Having established this point, we consider the question from different perspectives. In the first part, game theory, or to be more precise, focal points theory, is used to determine the cognitive heuristics which help musicians in the coordination task. Then we show in the second part that the very idea of coordination is central to the formal dynamics of collective free improvisation. This theorical framework is finally completed by two kinds of empirical data : the analysis of Company Week's excerpts, a festival founded by guitarist Derek Bailey, in the third part ; and the results of five proto-experimentations conducted with musicians from both the Norwegian Academy and Lyon's CNSMD, in the fourth part.
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Teoria dos jogos aplicada: debates políticos televisivos / Applied game theory: televised political debatesOto Murer Küll Montagner 06 February 2017 (has links)
O presente trabalho busca apresentar uma aplicação da teoria dos jogos, de modo a complementar a literatura que utiliza esse referencial teórico e alcançar conclusões pertinentes que desafiam o senso comum. O assunto trabalhado são os debates políticos televisivos e o excesso de acusações realizadas pelos participantes. Através de premissas e expectativas dos jogos não cooperativos, que foram aplicadas sobre os debates de 2º turno das eleições presidenciais de 1989, 2006, 2010 e 2014, a hipótese de que a razão de tal comportamento é a própria organização do jogo, e não uma eventual falta de propostas a serem apresentadas pelos políticos, não é refutada empiricamente. Além disso, sugestões de mudanças de regras desses programas são realizadas, de modo que seu objetivo principal, a exposição de planos de governo, passe a ser atingido. / The present work seeks to present an application of the Game Theory, in order to complement the literature that uses this theoretical reference and to reach pertinent conclusions that defy common sense. The topic that is going to be studied are the televised political debates and the excess of accusations made by the participants. Through assumptions and expectations of non-cooperative games, that were applied to the 2nd round debates of the 1989, 2006, 2010 and 2014 presidential elections, the hypothesis that the reason for such behavior is the organization of the game, not an eventual lack of proposals by the political parties, is not empirically refuted. In addition, suggestions for changes in the rules of these programs are made, in order to ensure that the primary debates\' goal of exposing government plans is reached.
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Localização horizontal de produtos sob efeito de rede / Horizontal localization of products under network effectsDaniel Spinoso Prado 26 July 2016 (has links)
O modelo a ser apresentado consiste em um jogo de preço e localização entre duas firmas. Utiliza-se o pressuposto de que os consumidores têm sua utilidade positivamente afetada por um efeito de rede, ou seja, são diretamente influenciados pela tamanho da demanda do bem. Dispondo os consumidores uniformemente distribuídos dentro de um intervalo linear [0, 1], buscamos encontrar os equilíbrios de preço e localização do jogo proposto. Verificamos que, dados os pressupostos do modelo, existem equilíbrios de Nash para cada subjogo e dependerão da força dos efeitos de rede. Quando os efeitos de rede são fortes o suficiente, os preços praticados serão inicialmente reduzidos até que o monopólio seja alcançado por uma das firmas, quando o preço será elevado e a outra firma passará a cobrar um preço nulo. No subjogo de localizações foi possível identificar que, no caso em que o poder do efeito de rede está acima de um determinado nível, as firmas não irão diferenciar seus produtos e se localizarão em algum ponto dentro do intervalo fechado [1/4 , 3/4] / The model to be presented is a price-location game between two firms. The assumption is that consumers\' utility is positively affected by a network effect, i.e. it is directly influenced by the size of demand. Distributing consumers uniformly in a linear interval [0, 1] we seek the price and location equilibrium of the proposed game. We found that, given the model assumptions, there are Nash equilibria for each subset that depend on the strength of network effects. When network effects are strong enough, prices are initially reduced until the monopoly is reached by one of the firms, then the price rises and the other firm shall charge a null price. In the subgame of locations, when the power of the network effect is above a certain level, the firms will not differentiate their products and will be located at any point within the closed interval [1/4 , 3/4]
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