At the close of 1946, a year marked by domestic white-on-black violence, Harry S. Truman, in a dramatic move, established the President’s Committee on Civil Rights (PCCR). Five years before, his predecessor Franklin D. Roosevelt had formed the Fair Employment Practices Committee (FEPC), under pressure from civil rights groups mobilized against racial discrimination in the defense industry. The FEPC was the first major federal civil rights legislation since Reconstruction. However, when race riots later erupted in cities across the country in 1943, Roosevelt ignored his staff's recommendation to appoint a national race relations committee. Instead, he agreed to a “maypole” committee, which was, in actuality, a decentralized network of individuals, including Philleo Nash, whose purpose was to anticipate and diffuse urban racial tensions in order to avert further race riots. Superficially, Truman's PCCR seemed to resemble Roosevelt's rather conservative race relations strategy of appointing a committee rather than taking direct action under the authority of the federal government. But, as this project will argue, Truman's PCCR represented a major, historical change in the approach to civil rights that would have a profound effect on activists, such as Dorothy Tilly and Frank Porter Graham, and the movement itself. Where FDR's committees were created to avoid further racial confrontations, Truman’s committee invited and ignited controversy. Its groundbreaking report, To Secure These Rights (TSTR), unequivocally declared the federal government as the guardian of all Americans’ civil rights. In essence, Truman’s PCCR elevated the civil rights dialogue to a national level by recasting the civil rights issue as an American problem rather than just a black-American problem. Moreover, TSTR attacked segregation directly, and challenged the federal government to take the lead by immediately desegregating the armed services. These radical recommendations came only six years after a reluctant FDR formed the FEPC and six and one-half years before the Unites States’ Supreme Court’s landmark ruling, Brown v. the Board of Education of Topeka, Kansas and the ensuing backlash. Thus, Truman’s PCCR and TSTR, in 1947, forged a new “civil rights frontier.”

Traditionally, most consumers of electricity pay for their consumption according to a fixed-rate. The few existing implementations of real time pricing have been restricted to large industrial consumers, where the benefits could justify the high implementation cost. With the advancement of Smart Grid technologies, large scale implementation of variable-rate metering will be more practical. Consumers will be able to control their electricity consumption in an automated fashion, where one possible scheme is to have each individual maximize their own utility as a noncooperative game. In this thesis, noncooperative games are formulated among the consumers of Smart Grid with two real-time pricing schemes, where the Nash equilibrium operation points are investigated for their uniqueness and load balancing properties. The first pricing scheme charges a price according to the average cost of electricity borne by the retailer and the second charges according to a time-variant increasing-block price. The zero revenue model and the constant revenue rate model, are the two revenue models being considered. The relationship between these games and certain congestion games, known as atomic flow games from the computer networking community, is demonstrated. It is shown that the proposed noncooperative game formulation falls under the class of atomic splittable flow games. It is shown that the Nash equilibrium exists for four different cases, with different pricing schemes and revenue models, and is shown to be unique for three of the cases, under certain conditions. It is shown that both pricing schemes lead to similar electricity loading patterns when consumers are interested only in the minimization of electricity costs. Finally, the conditions under which the increasing-block pricing scheme is preferred over the average cost based pricing scheme are discussed.

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

The research subject of the dissertation is the analysis of the model of heterogenous agents and its application for modelling stochastic Nash and Stackelberg equilibriums, applying the Monte Carlo method. The aim of the dissertation is to identify the impact of heterogeneous agents on the formation of the economic bubble, to create and examine algorithms for special bilevel stochastic programming problems and for search of the stochastic Nash equilibrium, applying the Monte Carlo method. The thesis offers a mathematical model for identification of the beginning of the bubble. This model has been applied for the analysis of the real estate bubble in Lithuania. In cases of uncertainty, decisions are often made by several individuals whose interests do not coincide. In such situations one of the concepts of the equilibrium is the stochastic Nash equilibrium. The dissertation examines the stochastic Nash equilibrium and offers the algorithm for gradient search of this equilibrium. The algorithm for gradient search of the stochastic Nash equilibrium was examined by solving the problem of electricity market with precedent agreements. The dissertation offers the algorithm for solving the optimization problem where the objective function and constraints contain conditional value at risk and by solving the test problem the behaviour of the algorithm is investigated. The dissertation proposes the algorithm for solving the two stage stochastic linear problem, employing the method of... [to full text] / Disertacijos objektas – heterogeninių agentų modelio tyrimas ir taikymas stochastinėms Nešo ir Stakelbergo pusiausvyroms modeliuoti Monte Karlo metodu. Darbo tikslas – nustatyti heterogeninių agentų įtaką ekonominio burbulo susidarymui, sukurti ir ištirti dviejų lygių stochastinio programavimo specialių uždavinių bei stochastinės Nešo pusiausvyros paieškos Monte Karlo algoritmus. Netvarių būsenų (burbulų ir jų griūčių) identifikavimas labai svarbus ekonomikai bei finansams. Disertacijoje pateiktas burbulo pradžios identifikavimo matematinis modelis, kurį taikant buvo ištirtas Lietuvos nekilnojamojo turto burbulas. Esant neapibrėžtumui, sprendimus dažnai priima keli individai, kurių interesai nesutampa. Tokiose situacijose taikoma viena iš pusiausvyros koncepcijų, būtent, stochastinė Nešo pusiausvyra. Darbe ištirta stochastinė Nešo pusiausvyra ir pasiūlytas jos gradientinės paieškos algoritmas. Stochastinės Nešo pusiausvyros gradientinės paieškos algoritmas ištirtas sprendžiant elektros rinkos su išankstiniais sandoriais uždavinį. Optimizavimo uždavinys, kurio tikslo funkcijoje ir ribojimuose yra sąlyginės rizikos reikšmė yra dviejų lygių stochastinio programavimo uždavinys. Disertacijoje pasiūlytas tokio uždavinio sprendimo algoritmas ir testiniu uždaviniu ištirta jo elgsena. Jei stochastinis dviejų etapų tiesinis uždavinys sprendžiamas reikšmingų imčių metodu, tai gaunamas dviejų lygių stochastinio programavimo uždavinys. Disertacijoje pasiūlytas stochastinio dviejų etapų... [toliau žr. visą tekstą]

In this thesis, competitive and cooperative newsboy problems for two substitutable products are analyzed by using game theoretic concepts. The demands of the products are assumed to be dependent and normally distributed. Competition is handled for Nash and Stackelberg games. Nash and Stackelberg games are compared in terms of the order quantities and the expected profits. Cooperative newsboy problem is analyzed for the products having equal costs and revenues. The effect of demand correlation on the order quantities and the expected profits in all of the games is investigated through numerical experiments. Optimal solutions of the Nash, Stackelberg and the cooperative games are examined analytically when the demand correlation is 1.

This thesis consists of five chapters, based on four different articles. All of them are devoted to different aspects of spatial heterogeneity and its impact on economic equilibrium in space. The concept of heterogeneous continuous space is discussed in the introductory chapter.The first model "Equilibrium in Continuous Space under Decentralized Production" addresses the issue of the impact of differences across locations in exogeneous productivity on the structure of equilibrium prices, production and trade. The goal is to describe the general equilibrium in a spatially decentralized economy, when production, consumption and markets are distributed in continuous space and transportation costs are essentially linear. It is shown that an autarky equilibrium can exist only if transport costs are high enough. In the general case, the general equilibrium in this model includes some endogeneously determined trade areas, with flows of goods across space, and autarky areas where production and consumption activities take place only at the same point. An analytical solution in explicit functions is obtained; it contains equilibrium prices, labor supply and flows of goods as functions of the spatial variable. The model can be applied to a set of practical questions in regional economics. In particular, it is able to describe persistent price differentials across regions and non-local consequences of road construction and transportation cost shocks for the economy. The differences across locations in population density may have either historical or economic reasons.The second model "Hotelling's Revival" extends a well-known research of H.Hotelling (1929) to the two-dimensional case with spatially heterogeneous demand density, preserving the rest of his classical assumptions. It is shown that the problem of demand discontinuity in the one-dimensional model, which was discovered by d'Aspremont, Gabszewich and Thisse (1979), disappears in this case. This also holds for any bounded distribution of consumers on any compact set on a plane, which can describe real geographical situations. Demand continuity still holds for any transport costs, strictly increasing in distance and not necessarily linear. Although this is sufficient for the existence of Nash equilibrium in mixed strategies, in pure strategies it exists only for some subset of cases. Examples of both existence and non-existence are constructed, and for some family of densities the separation point between the two cases is found.The third model addresses locational choice of heterogeneous consumers, when land is also heterogeneous in quality. It is based on two articles. The first, "Dacha Pricing", is presented in chapter 4 and studies the problem of locational rent in a city-neighbourhood when utility includes both the impact of transport costs and time for transportation. For the case of identical agents the problem is solved explicitly and comparative statics with respect to exogeneous changes in transport cost and speed is studied. For the case of agents who are heterogeneous with respect to their income, a solution is also obtained. The model explains some evidence about dacha pricing in Russia and its dynamics during the transition period. The second article related to this model is "Location and Land Size Choice by Heterogeneous Agents". It generalizes the first one and form a separate chapter 5. A new approach about the general equilibrium allocation of heterogeneous divisible good (like land) among a continuum of heterogeneous consumers is proposed. The model is based on continuity of primitives which allow not only to finding a general equilibrium solution in a class of continuous functions, but also to treat the solution to a continuous problem as the limit of the corresponding sequence of discrete problems. This solves one of Berliant's paradoxes, related to spatial economics. The multiplicity of equilibria is shown to take place.

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

Le premier chapitre, en français, présente les principaux outils mathématiques utilisés dans le manuscrit, les résultats classiques sur la rationalité coalitionnelle pour les jeux coopératifs à utilité transférable et notamment sur le cœur et ses extensions, quelques résultats nouveaux sur le cœur k-additif et l’implémentation en équilibre de Nash fort de solutions de jeux coopératifs. Il y est synthétisé, sans démonstrations, les résultats des trois articles ainsi que quelques résultats nouveaux ou complémentaires. Les trois chapitres suivants, en anglais, correspondent aux trois articles. L’annexe A donnera en anglais les démonstrations des résultats nouveaux et non contenus dans les articles. / The first chapter, in french, presents the main mathematics tools used for this thesis, some classical results about coalitional rationality for cooperative TU-games, and among other things, about the core and its extensions. This chapter presents also some new or less known results about the k-additive core and strong Nash implementation of some cooperative games’ solutions. In addition, we summurize, without proofs, the main results which are contained in the three articles and some extra results that can be read in english in the appendix A. The three next chapters, in english, are the three articles. The Appendix A gives, in english, the proof of some extra results.

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Submitted by Lucas Alves Estevam de Lima (lucasaelima@gmail.com) on 2015-07-06T18:54:09Z No. of bitstreams: 1 dissertacao_lucas.pdf: 1226857 bytes, checksum: 0bfcc2903f4c75498fd9961c5b53ae21 (MD5) / Approved for entry into archive by BRUNA BARROS (bruna.barros@fgv.br) on 2015-07-07T12:23:12Z (GMT) No. of bitstreams: 1 dissertacao_lucas.pdf: 1226857 bytes, checksum: 0bfcc2903f4c75498fd9961c5b53ae21 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2015-07-09T12:13:05Z (GMT) No. of bitstreams: 1 dissertacao_lucas.pdf: 1226857 bytes, checksum: 0bfcc2903f4c75498fd9961c5b53ae21 (MD5) / Made available in DSpace on 2015-07-09T12:13:15Z (GMT). No. of bitstreams: 1 dissertacao_lucas.pdf: 1226857 bytes, checksum: 0bfcc2903f4c75498fd9961c5b53ae21 (MD5) Previous issue date: 2015-04-29 / This dissertation presents a alternative approach to deai with family taxation probiem. More specifically we modei lhe family decision as a Nash Bargaining where the pianner can choose optimally lhe disagreement utilities. We prove a Reveiation Principie for this modei so we can consider a smaller set of mechanisms, besides that we compute optimai mechanism gains compareci to other reasonabie mechanism through exampies. We discuss some implications o f lhe optimai mechanism. / Esta dissertação apresenta uma abordagem alternativa para o problema de taxação de famílias. Mais especificamente modelamos a decisão familiar com um modelo de barganha de Nash em que os o governo determina de forma ótima as utilidades de discórdia. Demonstramos um Princípio da Revelação para esse modelo de forma a reduzir a classe de mecanismos possíveis, além disso calculamos os ganhos do mecanismo ótimo em relação a outros mecanismos razoáveis por meio de exemplos. Discutimos algumas implicações associadas ao mecanismo ótimo.