Lean Startup is a widely adopted method nowadays, which contains a consistent approach to unveil a valid business model in a scenario of extreme uncertainty. This process involves a significant amount of effectual reasoning. On the other hand, established companies use planning strategies for their operations where causal reasoning drives the decision-making process based on future market predictions. There is clearly a gap on how growing startups that have discovered a working business model shift their initial effectual methodologies to more causal methods while they grow. In this thesis, common effectual and causal methodologies are explained and mapped against existing frameworks used in the industry. Furthermore, an analysis of how companies can include causality into the effectual methodologies initially used is done, in particular using the Lean Startup framework. Furthermore, the intrusion of causal components in effectual frameworks leads to a question of balancing between the causal and effectual components. A simple method to detect whether a startup needs one or the other during its evolution is presented and explained using game theory. Through non-cooperative game strategies, i.e. Nash equilibrium, a simple rule to evaluate the current balance between causation and effectuation can be used.

In this study, I introduce the alternative-dependent focal Luce model (ADFLM), a random choice model generalizing the well-known Luce model (1959). In the ADFLM, focal alternatives are chosen more frequently relative to their utilities. I identify utilities, focal sets, and the magnitude of focal biases from choice data. Additionally, I axiomatically characterize the ADFLM by weakening the independence of irrelevant alternatives (IIA) axiom. This model can explain the well-known behavioral phenomena, the attraction and compromise effects. Furthermore, I also study the seller's profit maximization problem in the ADFLM. I also study an asymmetric dynamic patent race with a deadline under complete information. In my model, two firms decide whether to invest in RandD. The patent arrives randomly according to a Poisson process, and the large firm has a higher hazard rate than the small firm. I find the unique sub-game perfect Nash equilibrium strategy for this game. At the equilibrium, the large firm will stay longer in the race, while the small firm will quit earlier. The large firm's optimal stopping time is not affected by the competition, while the small firm's stopping time is reduced. Additionally, I find that companies will remain longer in the race if the investigation cost is lower, the winning premium is higher, the deadline is extended further, and the hazard rate is more prominent. Moreover, the market becomes more efficient with the competition since the patent is easier to realize. / Doctor of Philosophy / In this research, I study the consumer's behavior when individuals have limited cannot or do not give the same attention to each alternative available to them. In my study, I characterize the alternative-dependent focal Luce model (ADFLM), a consumer behavior model. Moreover, I solve the seller's profit maximization problem when the consumer's behavior follows the ADFLM. Meanwhile, I also study a dynamic patent race problem that occurs when firms compete for a patent with a deadline. If no firms achieve the patent, the stopping time (when the firm quits the patent race) of the large firm's (with a higher success rate every period) is not affected by the introduction of the small firm. However, the small firm quits earlier when the large firm is introduced. The competition between the two companies increases the overall probability of receiving a patent.

Efficient algorithms exist for finding optimal strategies in extensive-form games. However human scale problems, such as poker, are typically so large that computation of these strategies remain infeasible with current technology. State space abstraction techniques allow us to derive a smaller abstract game, in which an optimal strategy can be computed and then used in the real game. This thesis introduces state of the art abstraction techniques. Most of these techniques do not deal with public information. We present a new automatic public state space abstraction technique. We examine the quality of this technique in the domain of poker. Our experimental results show that the new technique brings significant performance improvement. Powered by TCPDF (www.tcpdf.org)

Esta tese é um estudo acerca do Problema de Equilíbrio de Nash Generalizado (GNEP). Na primeira parte, faremos um resumo dos principais conceitos sobre GNEPs, a relação com outros problemas já conhecidos e comentaremos brevemente os principais métodos já feitos até esta data para resolver numericamente este tipo de problema. Na segunda parte, estudamos condições de otimalidade e condições de qualificação (CQ) para GNEPs, fazendo uma analogia como em otimização. Estendemos os conceitos de cone tangente, normal, gerado pelas restrições ativas, linearizado e polar para a estrutura dos GNEPs. Cada CQ de otimização gera dois tipos de CQ para GNEPs, sendo que a denotada por CQ-GNEP é mais forte e útil para a análise de algoritmos para GNEPs. Mostramos que as condições de qualificação para GNEPs deste tipo em alguns casos não guardam a mesma relação que em otimização. Estendemos também o conceito de Aproximadamente Karush-KuhnTucker (AKKT) de otimização para GNEPs, o AKKT-GNEP. É bem conhecido que AKKT é uma genuína condição de otimalidade em otimização, mas para o caso dos GNEPs mostramos que isto não ocorre em geral. Por outro lado, AKKT-GNEP é satisfeito, por exemplo, em qualquer solução de um GNEP conjuntamente convexo, desde que seja um equilíbrio bvariacional. Com isso em mente, definimos um método do tipo Lagrangiano Aumentado para o GNEP usando penalidades quadráticas e exponenciais e estudamos as propriedades de otimalidade e viabilidade dos pontos limites de sequências geradas pelo algoritmo. Finalmente alguns critérios para resolver os subproblemas e resultados numéricos são apresentados. / This thesis is a study about the generalized Nash equilibrium problem (GNEP). In the first part we will summarize the main concepts about GNEPs, the relationship with other known problems and we will briefly comment on the main methods already done in order to solve these problems numerically. In the second part we study optimality conditions and constraint qualification (CQ) for GNEPs making an analogy with the optimization case. We extend the concepts of the tangent, normal and generated by the active cones, linear and polar cone to the structure of the GNEPs. Each optimization CQ generates two types of CQs for GNEPs, with the one called CQ-GNEP being the strongest and most useful for analyzing the algorithms for GNEPs. We show that the qualification conditions for GNEPs of this type in some cases do not have the same relation as in optimization. We also extend the Approximate Karush- Kuhn-Tucker (AKKT) concept used in optimization for GNEPs to AKKT-GNEP. It is well known that AKKT is a genuine optimality condition in optimization but for GNEPs we show that this does not occur in general. On the other hand, AKKT-GNEP is satisfied, for example, in any solution of a jointly convex GNEP, provided that it is a b-variational equilibrium. With this in mind, we define Augmented Lagrangian methods for the GNEP, using the quadratic and the exponential penalties, and we study the optimality and feasibility properties of the sequence of points generated by the algorithms. Finally some criteria to solve the subproblems and numerical results are presented.

Uma solução para a preservação das águas é o investimento em saneamento e no tratamento do esgoto sanitário, que é realizado por meio de estações de tratamento de esgoto. Todavia, a escolha do sistema de tratamento a ser implantado em um município deve atender aos requisitos técnicos, ambientais, sociais e econômicos do mesmo. O objetivo principal desta pesquisa foi validar e avaliar a aplicabilidade de um modelo de tomada de decisão para escolha de sistema de tratamento de esgoto sanitário de menor custo econômico desenvolvido por Oliveira (2004). Este modelo elabora o dimensionamento de oito sistemas de tratamento e, a partir desses dados, faz a estimativa do custo de implantação, manutenção e operação de cada sistema. Para esta avaliação, foram realizadas entrevistas em órgãos relacionados a saneamento no Brasil, bem como com tomadores de decisão e especialistas em saneamento, a fim de coletar os dados necessários para aplicação de testes com o modelo. No total, foram coletados dados de 61 projetos de estações de tratamento de esgoto, os quais foram utilizados nos testes realizados. Durante a avaliação do modelo, foram utilizadas técnicas como simulação, análise hierárquica de processos e equilíbrio de Nash, além de serem realizados ajustes nos custos do modelo, nas variáveis utilizadas, nos sistemas de tratamento, dentre outras, totalizando 12 novas versões até a final, denominada ETEX-FEARP. Com base nas análises realizadas neste trabalho, considera-se o modelo adequado para proporcionar uma visão global no planejamento dos investimentos, bem como para estudos de concepções de estações de tratamento, auxiliando o tomador de decisão na escolha do sistema, com base em critérios econômicos, ambientais e técnicos. / A solution for the preservation of the water is the investment in sanitation and in the treatment of sanitary sewer, which is accomplished through sewer treatment stations. However, the choice of the treatment system to be implanted in a municipal district should meet its technical, environmental, social and economical requirements. The main objective of this research was to validate and to evaluate the applicability of a decision making model to choose the system of sanitary sewer treatment with the lowest economical cost developed by Oliveira (2004). This model elaborates the sizing of eight treatment systems, and then it estimates the implantation cost, maintenance and operation of each system. For this evaluation, interviews were performed in institutions related to sanitation in Brazil, as well as with decision makers and specialists in sanitation, in order to collect the necessary data for application of tests with the model. In the total, data from 61 projects of sewer treatment stations were collected, which were used in the accomplished tests. During the evaluation of the model, techniques such as simulation, hierarchical analysis of processes and Nash equilibrium were used. In addition, changes have been made in the costs of the model, in the used variables, in the treatment systems, among others, totaling 12 new versions, and the final version, was denominated \"ETEX-FEARP\". Based on the analysis done in this research, the model is considered appropriate to provide a global vision in the planning of the investments, as well as for studies of conceptions of treatment stations, helping the decision maker choose the system, based on economical, environmental and technical criteria.

Para auxiliar os gestores das organizações em seu processo decisório, o emprego de métodos de apoio à tomada de decisão é utilizado desde o século passado, a partir da década de 1950, havendo forte ênfase nas questões econômico-financeiras e operacionais das alternativas. Atualmente, o uso de métodos que consideram as questões relativas à sustentabilidade ambiental das alternativas é um assunto que tem despertado interesse, conforme se observa na literatura recente, ainda que relativamente escassa. Contudo, a práxis da maioria dos métodos multicritério existentes tem embasamento no tomador de decisão como um indivíduo ao invés de um grupo e a ampla diferença entre o comportamento de um indivíduo e de um grupo é negligenciado. Neste novo tipo de abordagem, soluções para resolver os conflitos que inevitavelmente surgem da necessidade de atender os diferentes critérios dos agentes envolvidos devem ser propostas. Para estes casos, a Teoria dos Jogos é reconhecidamente uma abordagem que permite a resolução de conflitos por meio da avaliação de diferentes cenários com diferentes alternativas. Neste sentido, a presente pesquisa apresenta um método multicriterial, baseado em indicadores de sustentabilidade em conjunto com a Teoria dos Jogos e o equilíbrio de Nash, para que seja uma das ferramentas de apoio na escolha do sistema de tratamento de esgoto sanitário para municípios. Para tornar possível a metodologia proposta, indicadores de sustentabilidade foram selecionados para serem usados como critérios na avaliação de alternativas de sistema de tratamento de esgoto. Além disto, vetores de pesos para os critérios foram definidos para representar perfis de jogadores. A partir disto, foi proposta uma função de pagamentos e um exemplo foi gerado a partir da definição do jogo e seus jogadores, tendo sido o software Gambit utilizado para encontrar o equilíbrio de Nash do jogo. Como resultado, a aplicação da metodologia proposta permite tratar o processo de escolha de ETE como um processo de escolha em grupo, ao invés de uma escolha individual, e visa contribuir para quebrar o paradigma da busca pela eficiência baseada nos critérios formados pelo binômio técnico e econômico na escolha de sistemas de tratamento de esgoto. Desta forma, a aplicação do novo método visa proporcionar meios para se enxergar o mesmo problema sobre diferentes focos e, com a utilização de diferentes critérios, poderia facilitar o processo da tomada de decisão para a escolha da alternativa técnica, econômica, ambiental e socialmente mais adequada. / To assist the managers of organizations in their decision making, the use of methods to support the decision are used since the last century, from the 1950s, with a strong emphasis on economic issues, financial and operational details of the treatment plants sewage. Currently, the use of methods to consider issues relating to the environmental sustainability of wastewater treatment plants is a subject that has attracted attention, as shown in recent studies, although relatively scarce. However, the practice of most existing methods are based on multicriteria decision-maker as an individual instead of a group and the wide difference between the behavior of an individual and a group is neglected. In this new approach, solutions to resolve the conflicts that inevitably arise from the need to meet the various criteria of the parties involved must be proposed. For these cases, game theory is admittedly an approach that allows the resolution of conflicts through the evaluation of different scenarios with different alternatives. With this research we sought to develop a measurement methodology based on indicators of sustainability in conjunction with game theory and Nash equilibrium, that is one of tools to support the choice of system of sewage treatment for a particular municipality . For the proposed new methodology, sustainability indicators were selected to be used as criteria in the evaluation of alternative system of sewage treatment and weight vectors for the criteria were defined as profiles of players. From this, we choose a function of reward and an example was generated from the definition of the game and its players, the software Gambit was used to find the Nash equilibrium of the game. The proposed methodology allows us to treat the process of choosing ETE as a selection process in group, rather than an individual choice, and aims to deconstruct the paradigm of the quest for efficiency based on criteria formed the duo in the technical and economic choice of systems for wastewater treatment. Thus, applying the new method aims at providing means to see the same problem on different sides, and with the use of different criteria, could facilitate the process of decision making for the choice of alternative technical, economic, environmental and socially suitable.

Orientador: Prof. Dr. Sinuê Dayan Barbero Lodovici / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional - PROFMAT, 2014. / Os jogos encantam a humanidade desde os tempos mais remotos. Especialmente, os jogos abstratos (ou matemáticos) atraíram a atenção de matemáticos ilustres como Bernoulli, dentre tantos. E esta atração deu origem a novas áreas da matemática, em destaque, surgiu também a Teoria dos Jogos. Esta teoria trás a beleza de transformar interações humanas em jogos, modelando fenômenos que podem ser observados quando dois ou mais "agentes de decisão" interagem entre si com conflitos e/ou cooperação. O estudo da Teoria dos Jogos utiliza recursos da modelagem matemática equacionando diferentes situações de diferentes campos de estudo e é esta característica interdisciplinar que inspirou este trabalho. A Teoria dos Jogos vem sendo utilizada em várias áreas, como economia, biologia, sociologia, etc. Neste trabalho pretende-se passar as noções básicas da Teoria dos Jogos para professores do ensino básico como uma possível ferramenta para fomentar entre os educandos o interesse pela matemática aplicada além deles serem beneficiados pelo desenvolvimento do pensamento estratégico, da atenção, raciocínio lógico, planejamento de ação e sequenciamento, habilidades muito úteis na competência de resolver problemas. Almeja-se que aconteça a construção do conhecimento dos alunos de uma forma mais atraente / The games enchanted mankind since ancient times. Especially, abstract games (or mathematical) attracted the attention of illustrious mathematicians like Bernoulli, among many. And this attraction gave rise to new areas of mathematics, highlighted, also appeared to Game Theory. The theory behind the beauty of transforming human interactions in games, modeling phenomena that can be observed when two or more "decision-makers" interact with conflict and / or cooperation. The study of Game¿s Theory uses mathematical modeling resources equating different situations of different fields of study and this interdisciplinary characteristic that inspired this work. The Game¿s Theory has been used in various areas, such as economics, biology, sociology, etc. This paper intends spending the basics of Game¿s Theory to elementary school teachers as a possible tool to foster among the students, the interest in applied mathematics and these be benefited by the development of strategic thinking, attention, logical reasoning, planning action and sequencing, very useful skills in problemsolving competence. It¿s desire to happen the construction of students¿ knowledge in a more attractive way.

A competitive electricity market has been established in many European countries including the Czech Republic. The electricity market includes a limited number of significant producers and traders, which can be described by oligopoly model. Since the electricity transmission and distribution are regulated, I consider two types of players performing in the electricity market: producers of electricity and traders, who buy electricity from producers and sell it to final customers. I derive oligopoly model with producers and traders "a la Cournot" and calculate a formula of equilibrium strategies. I use these theoretical findings to build a dynamic oligopoly model Ele. Ele is formulated as a mixed complementary problem and calibrated on data for the Czech Republic and neighbor states for several scenarios. The model was specified and calculated in GAMS software by the PATH solver. The results represent a Nash equilibrium. That means for individual producers: electricity generation, investment in new power plants construction and emission permits purchases. For traders the results are: equilibrium purchases, sales and cross-border transfers of electricity in each particular time period. Ele derives also equilibrium regional wholesale and retail electricity prices, emission permit prices and prices of cross-border auctions. Ele results point to an economic profitability of new nuclear power plants constructions. Further, I formulate a game in short-term electricity market, where I advise to Czech market participants, subjects of settlement, how much and in which circumstances to buy or sell electricity. Equilibrium results obtained through simulations based on the principle of a fictive game show that the current payment system of imbalance in the Czech Republic does not increase the risk of instability of electricity networks.

Les défis auxquels sont confrontés les différents secteurs de l’économie, répondent à l'évolution et à la spécialisation des consommateurs et des producteurs, dont les besoins sont de plus en plus complexes. À cet égard, au cours des 5 dernières années, les marchés de l'électricité ont subi un processus évolutif qui vise à répondre aux besoins de tous les intervenants dans des scénarios de développement durable.Aussi les agents impliqués dans les marchés de l'électricité, exposés à des risques opérationnels, juridiques, éthiques, financiers, entre autres, doivent‐ils se spécialiser pour s'approprier notamment de nouvelles technologies. Cette recherche porte principalement sur l'étude du risque financier tout à s'attachant à prendre en compte les nombreuses spécificités des marchés de l'électricité dans le but d'assurer le bon fonctionnement du marché et de ses participants.Dans les développements antérieurs, certains modèles se sont concentrés sur les phénomènes de pannes de courant électrique, d'instabilité du réseau, de variations de puissance, de réseaux intelligents, entre autres. D'autres études ont abordé la question de la prédiction de variables comme le prix et la stratégie d'entreprise, dans le but d'accroître les profits des participants. Ce projet de thèse propose un modèle financier complexe, qui se traduit par le calcul d'un équilibre de marché à partir des conditions initiales et des contraintes de risque. En utilisant la théorie des jeux, nous expliquons l'instabilité de l’équilibre. Nous montrons, en dépit de la complexité, qu'il est possible de trouver un scénario optimal en termes de rentabilité pour le système et les agents.Ce travail est structuré de la façon suivante. Dans le premier chapitre, une revue des études antérieures est présentée afin d’établir le contexte de la recherche. Le chapitre 2 décrit le marché de l'électricité colombienne avec ses particularités. Dans le chapitre 3, les indicateurs de risque (KRI) sont définis. Ils constitueront une partie fondamentale du modèle complet présenté dans le chapitre 4. Enfin, le chapitre 5, d'une part, présente les résultats obtenus et, d'autre part, discute de différentes voies d'approfondissement. / The challenges faced by different sectors of the economy, respond to the evolution and specialization of consumers and producers, where the needs are becoming more complex. In this sense, during the last 5 years the electricity markets have undergone an evolutionary pro- cess that aims to meet the needs of all stakeholders in the midst of sustainability scenarios.Thus, the agents involved in the electricity market, present a num- ber of exhibitions of operational nature, legal, ethical, financial, among others, which require a specialization allowing the entry of new tech- nologies. This research project focuses on the study of financial risk, which despite being so specific, consider many elements with the aim of ensuring the functioning of the market and its participants.In previous studies, some models have concentrated on the in- vestigation of blackouts phenomena, the stability of the network, the dynamic power system, and Smart grids, among others. Mean- while other investigations have addressed the problem of forecasting different variables like the spot price and corporate strategy, with the aim of increasing the profitability of the participants. Now, this project presents the proposal of a complex financial model, which results in calculating a market equilibrium considering initial condi- tions and risk constraints. Using game theory it demonstrates equi- librium instability and that through complexity it is possible to find an optimal scenario in terms of profitability for the system and the agents.In chapter 1 it carried out a review of previous studies in order to justify the investigation, then Chapter 2 includes a description of the Colombian electricity market, with different specifications. In chap- ter 3 the KRI are defined, and they will be integrated in Chapter 4 as a fundamental part of the comprehensive model. Finally, Chapter 5 includes the results of the study ending with some possible further studies and additional considerations.

In the field of VLSI circuit optimization, the scaling of semiconductor devices has led to the miniaturization of the feature sizes resulting in a significant increase in the integration density and size of the circuits. At the nanometer level, due to the effects of manufacturing process variations, the design optimization process has transitioned from the deterministic domain to the stochastic domain, and the inter-relationships among the specification parameters like delay, power, reliability, noise and area have become more intricate. New methods are required to examine these metrics in a unified manner, thus necessitating the need for multi-metric optimization. The optimization algorithms need to be accurate and efficient enough to handle large circuits. As the size of an optimization problem increases significantly, the ability to cluster the design metrics or the parameters of the problem for computational efficiency as well as better analysis of possible trade-offs becomes critical. In this dissertation research, several utilitarian methods are investigated for variation aware multi-metric optimization in VLSI circuit design and spatial pattern clustering. A novel algorithm based on the concepts of utility theory and risk minimization is developed for variation aware multi-metric optimization of delay, power and crosstalk noise, through gate sizing. The algorithm can model device and interconnect variations independent of the underlying distributions and works by identifying a deterministic linear equivalent model from a fundamentally stochastic optimization problem. Furthermore, a multi-metric gate sizing optimization framework is developed that is independent of the optimization methodology, and can be implemented using any mathematical programming approach. It is generalized and reconfigurable such that the metrics can be selected, removed, or prioritized for relative importance depending upon the design requirements. In multi-objective optimization, the existence of multiple conflicting objectives makes the clustering problem challenging. Since game theory provides a natural framework for examining conflicting situations, a game theoretic algorithm for multi-objective clustering is introduced in this dissertation research. The problem of multi-metric clustering is formulated as a normal form multi-step game and solved using Nash equilibrium theory. This algorithm has useful applications in several engineering and multi-disciplinary domains which is illustrated by its mapping to the problem of robot team formation in the field in multi-emergency search and rescue. The various algorithms developed in this dissertation achieve significantly better optimization and run times as compared to other methods, ensure high utility levels, are deterministic in nature and hence can be applied to very large designs. The algorithms have been rigorously tested on the appropriate benchmarks and data sets to establish their efficacy as feasible solution methods. Various quantitative sensitivity analysis have been performed to identify the inter-relationships between the various design parameters.