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1
Terry, Elaine Audrey. "Problem solving methods in game theory." DigitalCommons@Robert W. Woodruff Library, Atlanta University Center, 1988. http://digitalcommons.auctr.edu/dissertations/1796.
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Game theory is the mathematical theory associated with winning strategic and non-strategic games. In order to win a game, a player must find an optimal strategy to play. Strategies may be either pure or mixed. The latter is used when there are no pure strategies available . Games that require mixed strategies may be solved by various methods.
This study is concerned with the basic theory of games. Definitions and methods for solving games are discussed. The methods for solving involve both pure and mixed strategies. The simplex method for solving linear programming problems is reviewed. The numerical examples were solved using the IBM Macintosh with the MacSimplex package.
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Cisneros-Molina, Myriam. "Mathematical methods for valuation and risk assessment of investment projects and real options." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491350.
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In this thesis, we study the problems of risk measurement, valuation and hedging of financial positions in incomplete markets when an insufficient number of assets are available for investment (real options). We work closely with three measures of risk: Worst-Case Scenario (WCS) (the supremum of expected values over a set of given probability measures), Value-at-Risk (VaR) and Average Value-at-Risk (AVaR), and analyse the problem of hedging derivative securities depending on a non-traded asset, defined in terms of the risk measures via their acceptance sets. The hedging problem associated to VaR is the problem of minimising the expected shortfall. For WCS, the hedging problem turns out to be a robust version of minimising the expected shortfall; and as AVaR can be seen as a particular case of WCS, its hedging problem is also related to the minimisation of expected shortfall. Under some sufficient conditions, we solve explicitly the minimal expected shortfall problem in a discrete-time setting of two assets driven by correlated binomial models. In the continuous-time case, we analyse the problem of measuring risk by WCS, VaR and AVaR on positions modelled as Markov diffusion processes and develop some results on transformations of Markov processes to apply to the risk measurement of derivative securities. In all cases, we characterise the risk of a position as the solution of a partial differential equation of second order with boundary conditions. In relation to the valuation and hedging of derivative securities, and in the search for explicit solutions, we analyse a variant of the robust version of the expected shortfall hedging problem. Instead of taking the loss function $l(x) = [x]^+$ we work with the strictly increasing, strictly convex function $L_{\epsilon}(x) = \epsilon \log \left( \frac{1+exp\{−x/\epsilon\} }{ exp\{−x/\epsilon\} } \right)$. Clearly $lim_{\epsilon \rightarrow 0} L_{\epsilon}(x) = l(x)$. The reformulation to the problem for L_{\epsilon}(x) also allow us to use directly the dual theory under robust preferences recently developed in [82]. Due to the fact that the function $L_{\epsilon}(x)$ is not separable in its variables, we are not able to solve explicitly, but instead, we use a power series approximation in the dual variables. It turns out that the approximated solution corresponds to the robust version of a utility maximisation problem with exponential preferences $(U(x) = −\frac{1}{\gamma}e^{-\gamma x})$ for a preferenes parameter $\gamma = 1/\epsilon$. For the approximated problem, we analyse the cases with and without random endowment, and obtain an expression for the utility indifference bid price of a derivative security which depends only on the non-traded asset.
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Kuipers, Jeroen. "Combinatorial methods in cooperative game theory." Maastricht : Maastricht : Datawyse/Universitaire Pers Maastricht ; University Library, Maastricht University [Host], 1994. http://arno.unimaas.nl/show.cgi?fid=6950.
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Deligiannis, Anastasios. "Mathematical optimization and game theoretic methods for radar networks." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/22732.
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Radar systems are undoubtedly included in the hall of the most momentous discoveries of the previous century. Although radars were initially used for ship and aircraft detection, nowadays these systems are used in highly diverse fields, expanding from civil aviation, marine navigation and air-defence to ocean surveillance, meteorology and medicine. Recent advances in signal processing and the constant development of computational capabilities led to radar systems with impressive surveillance and tracking characteristics but on the other hand the continuous growth of distributed networks made them susceptible to multisource interference. This thesis aims at addressing vulnerabilities of modern radar networks and further improving their characteristics through the design of signal processing algorithms and by utilizing convex optimization and game theoretic methods. In particular, the problems of beamforming, power allocation, jammer avoidance and uncertainty within the context of multiple-input multiple-output (MIMO) radar networks are addressed. In order to improve the beamforming performance of phased-array and MIMO radars employing two-dimensional arrays of antennas, a hybrid two-dimensional Phased-MIMO radar with fully overlapped subarrays is proposed. The work considers both adaptive (convex optimization, CAPON beamformer) and non-adaptive (conventional) beamforming techniques. The transmit, receive and overall beampatterns of the Phased-MIMO model are compared with the respective beampatterns of the phased-array and the MIMO schemes, proving that the hybrid model provides superior capabilities in beamforming. By incorporating game theoretic techniques in the radar field, various vulnerabilities and problems can be investigated. Hence, a game theoretic power allocation scheme is proposed and a Nash equilibrium analysis for a multistatic MIMO network is performed. A network of radars is considered, organized into multiple clusters, whose primary objective is to minimize their transmission power, while satisfying a certain detection criterion. Since no communication between the clusters is assumed, non-cooperative game theoretic techniques and convex optimization methods are utilized to tackle the power adaptation problem. During the proof of the existence and the uniqueness of the solution, which is also presented, important contributions on the SINR performance and the transmission power of the radars have been derived. Game theory can also been applied to mitigate jammer interference in a radar network. Hence, a competitive power allocation problem for a MIMO radar system in the presence of multiple jammers is investigated. The main objective of the radar network is to minimize the total power emitted by the radars while achieving a specific detection criterion for each of the targets-jammers, while the intelligent jammers have the ability to observe the radar transmission power and consequently decide its jamming power to maximize the interference to the radar system. In this context, convex optimization methods, noncooperative game theoretic techniques and hypothesis testing are incorporated to identify the jammers and to determine the optimal power allocation. Furthermore, a proof of the existence and the uniqueness of the solution is presented. Apart from resource allocation applications, game theory can also address distributed beamforming problems. More specifically, a distributed beamforming and power allocation technique for a radar system in the presence of multiple targets is considered. The primary goal of each radar is to minimize its transmission power while attaining an optimal beamforming strategy and satisfying a certain detection criterion for each of the targets. Initially, a strategic noncooperative game (SNG) is used, where there is no communication between the various radars of the system. Subsequently, a more coordinated game theoretic approach incorporating a pricing mechanism is adopted. Furthermore, a Stackelberg game is formulated by adding a surveillance radar to the system model, which will play the role of the leader, and thus the remaining radars will be the followers. For each one of these games, a proof of the existence and uniqueness of the solution is presented. In the aforementioned game theoretic applications, the radars are considered to know the exact radar cross section (RCS) parameters of the targets and thus the exact channel gains of all players, which may not be feasible in a real system. Therefore, in the last part of this thesis, uncertainty regarding the channel gains among the radars and the targets is introduced, which originates from the RCS fluctuations of the targets. Bayesian game theory provides a framework to address such problems of incomplete information. Hence, a Bayesian game is proposed, where each radar egotistically maximizes its SINR, under a predefined power constraint.
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Marston, Matthew C. "Game based design : a game theory based approach to engineering design." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/15877.
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Mehta, Aranyak. "Algorithmic Game Theory." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7220.
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The interaction of theoretical computer science with game theory and
economics has resulted in the emergence of two very interesting
research directions. First, it has provided a new model for algorithm
design, which is to optimize in the presence of strategic
behavior. Second, it has prompted us to consider the computational
aspects of various solution concepts from game theory, economics and
auction design which have traditionally been considered mainly in a
non-constructive manner. In this thesis we present progress along both
these directions. We first consider optimization problems that arise
in the design of combinatorial auctions. We provide an online
algorithm in the important case of budget-bounded utilities. This
model is motivated by the recent development of the business of online
auctions of search engine advertisements. Our algorithm achieves a
factor of $1-1/e$, via a new linear programming based technique to
determine optimal tradeoffs between bids and budgets. We also provide
lower bounds in terms of hardness of approximation in more general
submodular settings, via a PCP-based reduction. Second, we consider
truth-revelation in auctions, and provide an equivalence theorem
between two notions of strategy-proofness in randomized auctions of
digital goods. Last, we consider the problem of computing an
approximate Nash equilibrium in multi-player general-sum games, for
which we provide the first subexponential time algorithm.
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Jacquot, Paulin. "Game theory and Optimization Methods for Decentralized Electric Systems." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLX101/document.
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Dans le contexte de transition vers un système électrique décentralisé et intelligent, nous abordons le problème de la gestion des flexibilités de consommation électriques. Nous développons différentes méthodes basées sur l'optimisation distribuée et la théorie des jeux.Nous commençons par adopter le point de vue d'un opérateur central en charge de la gestion des flexibilités de plusieurs agents. Nous présentons un algorithme distribué permettant le calcul des profils de consommations des agents optimaux pour l'opérateur.Cet algorithme garantit la confidentialité des agents~: les contraintes individuelles, ainsi que le profil individuel de consommation de chaque agent, ne sont jamais révélés à l'opérateur ni aux autres agents.Ensuite, nous adoptons dans un second modèle une vision plus décentralisée et considérons un cadre de théorie des jeux pour la gestion des flexibilités de consommation.Cette approche nous permet en particulier de modéliser les comportements stratégiques des consommateurs.Dans ce cadre, une classe de jeux adéquate est donnée par les jeux de congestion atomiques fractionnables.Nous obtenons plusieurs résultats théoriques concernant les équilibres de Nash dans cette classe de jeux, et nous quantifions l'efficacité de ces équilibres en établissant des bornes supérieures sur le prix de l'anarchie.Nous traitons la question du calcul décentralisé des équilibres de Nash dans ce contexte en étudiant les conditions et les vitesses de convergence des algorithmes de meilleure réponse et de gradient projeté.En pratique un opérateur peut faire face à un très grand nombre de joueurs, et calculer les équilibres d'un jeu de congestion dans ce cas est difficile.Afin de traiter ce problème, nous établissons des résultats sur l'approximation d'un équilibre dans les jeux de congestion et jeux agrégatifs avec un très grand nombre de joueurs et en présence de contraintes couplantes.Ces résultats, obtenus dans le cadre des inégalités variationnelles et sous certaines hypothèses de monotonie, peuvent être utilisés pour calculer un équilibre approché comme solution d'un problème de petite dimension.Toujours dans la perspective de modéliser un très grand nombre d'agents, nous considérons des jeux de congestion nonatomiques avec contraintes couplantes et avec une infinité de joueurs hétérogènes~: ce type de jeux apparaît lorsque les caractéristiques d'une population sont décrites par une fonction de distribution paramétrique.Sous certaines hypothèses de monotonie, nous prouvons que les équilibres de Wardrop de ces jeux, définis comme solutions d'une inégalité variationnelle de dimension infinie, peuvent être approchés par des équilibres de Wardrop symétriques de jeux annexes, solutions d'inégalités variationnelles de petite dimension.Enfin, nous considérons un modèle de jeu pour l'étude d'échanges d'électricité pair-à-pair au sein d'une communauté de consommateurs possédant des actifs de production électrique renouvelable.Nous étudions les équilibres généralisés du jeu obtenu, qui caractérisent les échanges possibles d'énergie et les consommations individuelles.Nous comparons ces équilibres avec la solution centralisée minimisant le coût social, et nous évaluons l'efficacité des équilibres via la notion de prix de l'anarchieIn the context of smart grid and in the transition to decentralized electric systems, we address the problem of the management of distributed electric consumption flexibilities. We develop different methods based on distributed optimization and game theory approaches.We start by adopting the point of view of a centralized operator in charge of the management of flexibilities for several agents. We provide a distributed and privacy-preserving algorithm to compute consumption profiles for agents that are optimal for the operator.In the proposed method, the individual constraints as well as the individual consumption profile of each agent are never revealed to the operator or the other agents.Then, in a second model, we adopt a more decentralized vision and consider a game theoretic framework for the management of consumption flexibilities.This approach enables, in particular, to take into account the strategic behavior of consumers.Individual objectives are determined by dynamic billing mechanisms, which is motivated by the modeling of congestion effects occurring on time periods receiving a high electricity load from consumers.A relevant class of games in this framework is given by atomic splittable congestion games.We obtain several theoretical results on Nash equilibria for this class of games, and we quantify the efficiency of those equilibria by providing bounds on the price of anarchy.We address the question of the decentralized computation of equilibria in this context by studying the conditions and rates of convergence of the best response and projected gradients algorithms.In practice an operator may deal with a very large number of players, and evaluating the equilibria in a congestion game in this case will be difficult.To address this issue, we give approximation results on the equilibria in congestion and aggregative games with a very large number of players, in the presence of coupling constraints.These results, obtained in the framework of variational inequalities and under some monotonicity conditions, can be used to compute an approximate equilibrium, solution of a small dimension problem.In line with the idea of modeling large populations, we consider nonatomic congestion games with coupling constraints, with an infinity of heterogeneous players: these games arise when the characteristics of a population are described by a parametric density function.Under monotonicity hypotheses, we prove that Wardrop equilibria of such games, given as solutions of an infinite dimensional variational inequality, can be approximated by symmetric Wardrop equilibria of auxiliary games, solutions of low dimension variational inequalities.Again, those results can be the basis of tractable methods to compute an approximate Wardrop equilibrium in a nonatomic infinite-type congestion game.Last, we consider a game model for the study of decentralized peer-to-peer energy exchanges between a community of consumers with renewable production sources.We study the generalized equilibria in this game, which characterize the possible energy trades and associated individual consumptions.We compare the equilibria with the centralized solution minimizing the social cost, and evaluate the efficiency of equilibria through the price of anarchy
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Ahmed, Samah. "Perturbation field theory methods for calculating expectation values." Thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/26214.
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Marsh, Christopher D. "Counter piracy a repeated game with asymmetric information." Thesis, Monterey, California : Naval Postgraduate School, 2009. http://edocs.nps.edu/npspubs/scholarly/theses/2009/Sep/09Sep%5FMarsh.pdf.
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Thesis (M.S. in Operations Research)--Naval Postgraduate School, September 2009.Thesis Advisor(s): Lin, Kyle Y. "September 2009." Description based on title screen as viewed on 5 November 2009. Author(s) subject terms: Piracy, game theory, Bayesian update. Includes bibliographical references (p. 37-38). Also available in print.
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Huang, Yun, and 黄赟. "Game-theoretic coordination and configuration of multi-level supply chains." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B44904411.
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Maskery, Michael. "Game theoretic methods for networked sensors and dynamic spectrum access." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/210.
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Automated devices enabled by wireless communications are deployed for a variety of purposes.
As they become more ubiquitous, their interaction becomes increasingly important
for coexistence when sharing a scarce resource, and for leveraging potential cooperation to achieve larger design goals.
This thesis investigates the use of game theory as a tool for design and analysis of networked systems of automated devices
in the areas of naval defence, wireless environmental monitoring through sensor networks, and cognitive radio wireless communications.
In the first part, decentralized operation of naval platforms deploying
electronic countermeasures against missile threats is studied.
The problem is formulated as a stochastic game in which platforms independently plan and execute
dynamic strategies to defeat threats in two situations: where coordination is impossible due to lack of
communications, and where platforms hold different objectives but can coordinate, according
to the military doctrine of Network Enabled Operations.
The result is a flexible, robust model for missile deflection for advanced naval groups.
Next, the problem of cooperative environmental monitoring and communication in energy-constrained wireless sensor networks
is considered from a game-theoretic perspective. This leads to novel protocols in which sensors cooperatively trade off
performance with energy consumption with low communication and complexity overhead.
Two key results are an on-line adaptive learning algorithm for tracking the correlated equilibrium set of a slowly
varying sensor deployment game, and an analysis of the equilibrium properties of threshold policies in a
game with noisy, correlated measurements.
Finally, the problem of dynamic spectrum access for systems of cognitive radios is considered. A game theoretic formulation
leads to a scheme for competitive bandwidth allocation which respects radios' individual interests while enforcing fairness
between users. An on-line adaptive learning scheme is again proposed for negotiating fair, equilibrium resource allocations, while
dynamically adjusting to changing conditions.
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Nikram, Elham. "Three essays on game theory and computation." Thesis, University of Exeter, 2016. http://hdl.handle.net/10871/28755.
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The results section of my thesis includes three chapters. The first two chapters are on theoretical game theory. In both chapters, by mathematical modelling and game theoretical tools, I am predicting the behaviour of the players in some real world issues. Hoteling-Downs model plays an important role in the modern political interpretations. The first chapter of this study investigates an extension of Hoteling-Downs model to have multi-dimensional strategy space and asymmetric candidates. Chapter 3 looks into the inspection game where the inspections are not the same in the series of sequential inspections. By modelling the game as a series of recursive zero-sum games I find the optimal strategy of the players in the equilibrium. The forth chapter investigates direct optimization methods for large scale problems. Using Matlab implementations of Genetic and Nelder-Mead algorithms, I compare the efficiency and accuracy of the most famous direct optimization methods for unconstraint optimization problems based on differing number of variables.
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Kosko, Karl Wesley. "Mathematical Discussion and Self-Determination Theory." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/37551.
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This dissertation focuses on the development and testing of a conceptual framework for student motivation in mathematical discussion. Specifically, this document integrates Yackel and Cobbâ s (1996) framework with aspects of Self-Determination Theory (SDT), as described by Ryan and Deci (2000). Yackel and Cobb articulated the development of studentsâ mathematical dispositions through discussion by facilitating student autonomy, incorporating appropriate social norms and co-constructing sociomathematical norms. SDT mirrors these factors and describes a similar process of self-regulation through fulfillment of the individual needs of autonomy, social relatedness, and competence. Given the conceptual overlap, this dissertation examines the connection of SDT with mathematical discussion with two studies.
The first study examined the effect of student frequency of explaining mathematics on their perceived autonomy, competence and relatedness. Results of HLM analyses found that more frequent explanation of mathematics had a positive effect on studentsâ perceived mathematics autonomy, mathematics competence, and relatedness. The second study used a triangulation mixed methods approach to examine high school geometry studentsâ classroom discourse actions in combination with their perceived autonomy, competence, and relatedness. Results of the second study suggest a higher perceived sense of autonomy is indicative of more engagement in mathematical talk, but a measure of competence and relatedness are needed for such engagement to be fully indicative of mathematical discourse. Rather, students who lacked a measure of perceived competence or relatedness would cease participation in mathematical discussion when challenged by peers. While these results need further investigation, the results of the second study provide evidence that indicates the necessity of fulfilling all three SDT needs for engagement in mathematical discussion. Evidence from both the first and second studies presented in this dissertation provides support for the conceptual framework presented.Ph. D.
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Rodrigues, Sérgio da Silva. "Methods of nonlinear control theory in problems of mathematical physics." Doctoral thesis, Universidade de Aveiro, 2008. http://hdl.handle.net/10773/2931.
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Doutoramento em MatemáticaConsideramos a equação de Navier-Stokes num domínio bidimensional e estudamos a sua controlabilidade aproximada e a sua controlabilidade nas projecções em subespaços de campos vectoriais de dimensão finita. Consideramos controlos internos que tomam valores num espaço de dimensão finita. Mais concretamente, procuramos um subespaço de campos vectoriais de divergência nula de dimensão finita de tal modo que seja possível controlar aproximadamente a equação, através de controlos que tomam valores no mesmo subespaço. Usando algumas propriedades de continuidade da equação nos dados iniciais, nomeadamente a continuidade da solução quando o controlo varia na chamada métrica relaxada, reduzimos os resultados em controlabilidade à existência de um chamado conjunto saturante. Consideramos ambas as condições de fronteira do tipo Navier e Dirichlet homogéneas. Damos alguns exemplos de domínios e respectivos conjuntos saturantes. No caso especial das condições de fronteira do tipo Lions - um caso particular das condições do tipo Navier - através de uma técnica envolvendo perturbação analítica de métricas, transferimos a chamada controlabilidade nas projecções em espaços coordenados de dimensão finita de uma métrica para (muitas) outras.
We consider the Navier-Stokes equation on a two-dimensional domain and study its approximate controllability and its controllability on projections onto finite-dimensional subspaces of vector fields. We consider body controls taking values in a finite-dimensional space. More precisely we look for a finitedimensional subspace of divergence free vector fields that allow us to control approximately the equation using controls taking values in that subspace. Using some continuity properties of the equation on the initial data, namely the continuity of the solution when the control varies in so-called relaxation metric, we reduce the controllability issues to the existence of a so-called saturating set. Both Navier and no-slip boundary conditions are considered. We present some examples of domains and respective saturating sets. For the special case of Lions boundary conditions - a particular case of Navier boundary conditions - trough a technique involving analytic perturbation of metrics, we transfer so-called controllability on observed coordinate space from one metric to (many) other.
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Rittberg, Colin Jakob. "Methods, goals and metaphysics in contemporary set theory." Thesis, University of Hertfordshire, 2016. http://hdl.handle.net/2299/17218.
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This thesis confronts Penelope Maddy's Second Philosophical study of set theory with a philosophical analysis of a part of contemporary set-theoretic practice in order to argue for three features we should demand of our philosophical programmes to study mathematics. In chapter 1, I argue that the identification of such features is a pressing philosophical issue. Chapter 2 presents those parts of the discursive reality the set theorists are currently in which are relevant to my philosophical investigation of set-theoretic practice. In chapter 3, I present Maddy's Second Philosophical programme and her analysis of set-theoretic practice. In chapters 4 and 5, I philosophically investigate contemporary set-theoretic practice. I show that some set theorists are having a debate about the metaphysical status of their discipline{ the pluralism/non-pluralism debate{ and argue that the metaphysical views of some set theorists stand in a reciprocal relationship with the way they practice set theory. As I will show in chapter 6, these two stories are disharmonious with Maddy's Second Philosophical account of set theory. I will use this disharmony to argue for three features that our philosophical programmes to study mathematics should have: they should provide an anthropology of mathematical goals; they should account for the fact that mathematical practices can be metaphysically laden; they should provide us with the means to study contemporary mathematical practices.
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Alexandrova, Anna. "Connecting models to the real world game theory in action /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2006. http://wwwlib.umi.com/cr/ucsd/fullcit?p3205365.
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Thesis (Ph. D.)--University of California, San Diego, 2006.Title from first page of PDF file (viewed April 6, 2006). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 201-206).
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Pusa, Taneli. "Mathematical modelling of the impacts of environment using metabolic networks and game theory." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSE1011/document.
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Le sujet général de cette thèse est la modélisation mathématique des systèmes biologiques. Le principal modèle étudié est le réseau métabolique: une collection d'objets - métabolites, réactions biochimiques, enzymes et gènes - et les relations entre eux, généralement organisées sous forme de graphe.Trois sujets distincts sont couverts. Dans le premier chapitre principal, un algorithme appelé MOOMIN pour «Mathematical explOration of Omics data on a MetabolIc Network» est présenté. C'est un outil informatique permettant d'interpréter les résultats d'une analyse d'expression différentielle à l'aide d'un réseau métabolique. Le résultat de l'algorithme est un changement métabolique, exprimé en termes de réactions supposées avoir subi un changement d'activité, qui correspond le mieux aux données d'expression génique. Le deuxième chapitre principal traite de l'intersection de la théorie des jeux et de l'étude du métabolisme cellulaire. Un nouveau type de modèle est proposé, combinant les principes de la théorie des jeux évolutive à la modélisation par contraintes pour prédire le comportement métabolique. Dans le troisième et dernier chapitre principal, un modèle épidémiologique de l'agent pathogène de la vigne Xylella fastidiosa est présenté et analysé. À l'aide d'une analyse de sensibilité, l'importance relative des paramètres du modèle est évaluée et les résultats sont discutés du point de vue de la lutte contre la maladieThe overall subject of this thesis is mathematical modelling of biological systems. The main model under study is the metabolic network: a collection of objects — metabolites, biochemical reactions, enzymes, and genes — and the relations amongst them, usually organised to form a graph.Three distinct topics are covered. In the first main chapter, an algorithm called MOOMIN for “Mathematical explOration of Omics data on a MetabolIc Network” is presented. It is a computational tool to interpret the results of a differential expression analysis with the help of a metabolic network. The output of the algorithm is a metabolic shift, expressed in terms of reactions that were inferred to have undergone a change in activity, that best aligns with the gene expression data. In the second main chapter, the intersection of game theory and the study of cellular metabolism is discussed. A new type of model is proposed, one that combines the principles behind evolutionary game theory with constraint-based modelling to predict metabolic behaviour. In the third and last main chapter, an epidemiological model of the Xylella fastidiosa grapevine pathogen is presented and analysed. Using sensitivity analysis, the relative importance of the model parameters is evaluated, and the results discussed from the point of view of disease control
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TOSIN, ANDREA. "Discrete kinetic and stochastic game theory for vehicular traffic: Modeling and mathematical problems." Doctoral thesis, Politecnico di Torino, 2008. http://hdl.handle.net/11583/2623639.
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n this thesis we are concerned with the mathematical modeling of vehicular traffic atthe kinetic scale. In more detail, starting from the general structures proposed by Arlottiet al. and by Bellomo, we develop a discrete kinetic framework in which thevelocity of the vehicles is not regarded as a continuous variable but can take a finite number of values only. Discrete kinetic models have historically been conceived in connection with the celebrated Boltzmann equation, primarily as mathematical tools to reduce the analytical complexity of the latter (see e.g., Bellomo and Gatignol, Gatignol): The Boltzmann’s integro-differential equation is converted into a set of partial differential equations in time and space, which share with the former some good mathematical properties being at the same time easier to deal with. In the present context, however, the discretization of the velocity plays a specific role in modeling the system rather than being simply a mathematical simplification, because it allows one to relax the continuum hypothesis for the velocity variable and to include, at least partially, the strongly granular nature of the flow of cars in the kinetic theory of vehicular traffic. The discrete velocity framework also gives rise to an interesting structure of the interaction terms of the kinetic equations, which are inspired by the stochastic game theory.
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Basei, Matteo. "Topics in stochastic control and differential game theory, with application to mathematical finance." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3424239.
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We consider three problems in stochastic control and differential game theory, arising from practical situations in mathematical finance and energy markets.
First, we address the problem of optimally exercising swing contracts in energy markets. Our main result consists in characterizing the value function as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation. The case of contracts with penalties is straightforward. Conversely, the case of contracts with strict constraints gives rise to stochastic control problems where a non-standard integral constraint is present: we get the anticipated characterization by considering a suitable sequence of unconstrained problems. The approximation result is proved for a general class of problems with an integral constraint on the controls.
Then, we consider a retailer who has to decide when and how to intervene and adjust the price of the energy he sells, in order to maximize his earnings. The intervention costs can be either fixed or depending on the market share. In the first case, we get a standard impulsive control problem and we characterize the value function and the optimal price policy. In the second case, classical theory cannot be applied, due to the singularities of the penalty function; we then outline an approximation argument and we finally consider stronger conditions on the controls to characterize the optimal policy.
Finally, we focus on a general class of non-zero-sum stochastic differential games with impulse controls. After defining a rigorous framework for such problems, we prove a verification theorem: if a couple of functions is regular enough and satisfies a suitable system of quasi-variational inequalities, it coincides with the value functions of the problem and a characterization of the Nash equilibria is possible. We conclude by a detailed example: we investigate the existence of equilibria in the case where two countries, with different goals, can affect the exchange rate between the corresponding currencies.In questa tesi vengono considerati tre problemi relativi alla teoria del controllo stocastico e dei giochi differenziali; tali problemi sono legati a situazioni concrete nell'ambito della finanza matematica e, più precisamente, dei mercati dell'energia. Innanzitutto, affrontiamo il problema dell'esercizio ottimale di opzioni swing nel mercato dell'energia. Il risultato principale consiste nel caratterizzare la funzione valore come unica soluzione di viscosità di un'opportuna equazione di Hamilton-Jacobi-Bellman. Il caso relativo ai contratti con penalità può essere trattato in modo standard. Al contrario, il caso relativo ai contratti con vincoli stretti porta a problemi di controllo stocastico in cui è presente un vincolo non standard sui controlli: la suddetta caratterizzazione è allora ottenuta considerando un'opportuna successione di problemi non vincolati. Tale approssimazione viene dimostrata per una classe generale di problemi con vincolo integrale sui controlli. Successivamente, consideriamo un fornitore di energia che deve decidere quando e come intervenire per cambiare il prezzo che chiede ai suoi clienti, al fine di massimizzare il suo guadagno. I costi di intervento possono essere fissi o dipendere dalla quota di mercato del fornitore. Nel primo caso, otteniamo un problema standard di controllo stocastico impulsivo, in cui caratterizziamo la funzione valore e la politica ottimale di gestione del prezzo. Nel secondo caso, la teoria classica non può essere applicata a causa delle singolarità nella funzione che definisce le penalità. Delineiamo quindi una procedura di approssimazione e consideriamo infine condizioni più forti sui controlli, così da caratterizzare, anche in questo caso, il controllo ottimale. Infine, studiamo una classe generale di giochi differenziali a somma non nulla e con controlli di tipo impulsivo. Dopo aver definito rigorosamente tali problemi, forniamo la dimostrazione di un teorema di verifica: se una coppia di funzioni è sufficientemente regolare e soddisfa un opportuno sistema di disequazioni quasi-variazionali, essa coincide con le funzioni valore del problema ed è possibile caratterizzare gli equilibri di Nash. Concludiamo con un esempio dettagliato: indaghiamo l'esistenza di equilibri nel caso in cui due nazioni, con obiettivi differenti, possono condizionare il tasso di cambio tra le rispettive valute.
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Mao, Wen. "Essays on bargaining theory and voting behavior." Diss., Virginia Tech, 1994. http://hdl.handle.net/10919/38561.
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Elhedhli, Samir. "Interior-point decomposition methods for integer programming : theory and application." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37887.
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Mixed integer programming (MIP) provides an important modeling and decision support tool for a wide variety of real-life problems. Unfortunately, practical MIPs are large-scale in size and pose serious difficulties to the available solution methodology and software.This thesis presents a novel solution approach for large-scale mixed integer programming that integrates three bodies of research: interior point methods, decomposition techniques and branch-and-bound approaches. The combination of decomposition concepts and branch-and-bound is commonly known as branch-and-price, while the integration of decomposition concepts and interior point methods lead to the analytic centre cutting plane method (ACCPM). Unfortunately, the use of interior point methods within branch-and-bound methods could not compete with simplex based branch-and-bound due to the inability of "warm" starting.
The motivation for this study stems from the success of branch-and-price and ACCPM in solving integer and non-differentiable optimization problems respectively and the quest for a method that efficiently integrates interior-point methods and branch-and-bound.
The proposed approach is called an Interior Point Branch-and-Price method (IP-B&P) and works as follows. First, a problem's structure is exploited using Lagrangean relaxation. Second, the resulting master problem is solved using ACCPM. Finally, the overall approach is incorporated within a branch-and-bound scheme. The resulting method is more than the combination of three different techniques. It addresses and fixes complications that arise as a result of this integration. This includes the restarting of the interior-point methods, the branching rule and the exploitation of past information as a warm start.
In the first part of the thesis, we give the details of the interior-point branch-and-price method. We start by providing, discussing and implementing new ideas within ACCPM, then detail the IP-B&P method and its different components. To show the practical applicability of IP-B&P, we use the method as a basis for a new solution methodology for the production-distribution system design (PDSD) problem in supply chain management. In this second part of the thesis, we describe a two-level Lagrangean relaxation heuristic for the PDSD. The numerical results show the superiority of the method in providing the optimal solution for most of the problems attempted.
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Xue, Licun. "Coalitional stability in strategic situations." Thesis, McGill University, 1996. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=40287.
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In many (social, economic, and political) strategic situations, conflict and cooperations coexist and group (or coalitional) behavior is as important as individual behavior. This dissertation studies several issues in such situations.Chapter 1 provides an overview of the theoretical background and motivates the analysis undertaken.
Chapter 2 analyzes strategic situations with diverse coalitional interactions to ascertain the "stable" outcomes that will not be replaced by any rational (hence farsighted) coalition of individuals, and the coalitions that are likely to form. The analysis takes into full account the perfect foresight of rational individuals, which has been overlooked in the literature.
Chapter 3 defines "negotiation-proof Nash equilibrium", a notion that applies to environments where players can negotiate openly and directly prior to the play of a noncooperative game. The merit of the notion of negotiation-proof Nash equilibrium is twofold: (1) It resolves the nestedness and myopia embedded in the notion of coalition-proof Nash equilibrium. (2) The negotiation process, which is formalized by a "graph", serves as a natural alternative to the approach that models pre-play communication by an extensive form game.
Chapter 4 examines the notion of "renegotiation-proofness" in infinitely repeated games. It is shown that imposing renegotiation in all contingencies creates both conceptual and technical difficulties. A notion of self-enforcing agreements is offered: an agreement is self-enforcing if it is immune to any deviation by any coalition which cannot (confidently) count on renegotiation.
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Amidon, Bruce Douglas. "An economic analysis of counterfeit threaded fasteners in the construction industry." Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA231492.
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Thesis (M.S. in Management)--Naval Postgraduate School, June 1990.Thesis Advisor(s): Carrick, Paul M. Second Reader: Gates, William R. "June 1990." Description based on signature page on October 16, 2009. DTIC Descriptor(s): Mathematical models, industries, problem solving, screw threads, engineering, fastenings, game theory, force(mechanics), economic analysis, construction DTIC Indicator(s): Threaded fasteners, fasteners, game theory, theses Author(s) subject terms: Threaded fasteners; substandard fasteners; game theory Includes bibliographical references (p. 50-51). Also available online.
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Hartline, Jason D. "Optimization in the private value model : competitive analysis applied to auction design /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/7015.
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Singley, Andrew M. "Heuristic solution methods for the 1-dimensional and 2-dimensional mastermind problem." [Gainesville, Fla.] : University of Florida, 2005. http://purl.fcla.edu/fcla/etd/UFE0010554.
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韓祖淵 and Cho-yuen Han. "A unified game theory approach to H-infinity control and filtering." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31235815.
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Han, Cho-yuen. "A unified game theory approach to H-infinity control and filtering /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18635520.
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Ajmone, Marsan Giulia. "New paradigms and mathematical methods for complex systems in behavioral economics." Thesis, IMT Alti Studi Lucca, 2009. http://e-theses.imtlucca.it/49/1/Ajmone%20Marsan_phdthesis.pdf.
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This dissertation is devoted to the mathematical investigation of properties of complex socio-economic systems, where individual behaviors, and their interactions,
exert a crucial influence on the overall dynamics of the whole system. In order to understand the importance of such an investigation, it is necessary to briefly analyze some conceptual aspects relating to the interaction between applied mathematics and socio-economic sciences. The main issue in this field consists in coupling the usual qualitative interpretation of socio-economic phenomena with an innovative quantitative description by means of mathematical equations. This dialogue, however difficult, is necessary to reach a deeper understanding of socio-economic phenomena, where deterministic rules may be stochastically perturbed by individual behaviors. The difficulty mostly stems from the fact that the
behavior of socio-economic systems, where the collective dynamics differ from the sum of the individual behaviors, is a paradigmatic example of a complex system. These aspects are discussed in the introductory section that follows. The mathematical framework presented in this dissertation is built by suitable developments of the so-called mathematical kinetic theory for active particles,
which proved to be a useful reference for applications in many fields of life sciences. The description of a system by the methods of the mathematical kinetic theory essentially implies the definition of the microscopic state space of the interacting entities and of the distribution function over this state space. In the case of living systems, the identification of the microscopic state space
requires the definition of an additional variable, called activity, which captures the specific dynamical aspects of the system under consideration. Entities of living systems, called active particles, may be organized into several interacting populations. This dissertation presents in a unified context the results of the doctoral work, mostly described in four peer-reviewed research papers that are included as appendices of this dissertation. The essential ideas of each of the papers are introduced and summarized next. The first three papers exploit tools and developments of the kinetic theory for active particles, while the fourth paper is based on a different tool, namely on agents’ methods. The first paper,[3], develops a mathematical framework based on the kinetic theory for active particles, which describes the evolution of large systems of interacting entities. These entities are carriers of specific functions, in this case economic activities. The mathematical framework is constructed by means of a suitable decomposition into functional subsystems, namely aggregations of entities, which have the ability of expressing socio-economic purposes and unctions. The paper shows how this framework can be implemented to describe some specific complex economic applications. Specifically, the applications are focused on
opinion dynamics and job mobility phenomena. These two examples offer a first insight into multi-scale issues: starting from the application, a preliminary mathematical
framework which takes into account both microscopic and macroscopic interactions is developed. This framework may be adapted to a great variety of complex phenomena. The second paper,[4], contains the initial elements of the development of the mathematical theory for complex socio-economic systems, already introduced in the first paper. The approach is based on the methods of the mathematical
kinetic theory for active particles. The key concept of functional subsystem is analyzed in detail, developing suitable mathematical models, which involve the decomposition of the overall system into functional subsystems. Different examples of socio-economic phenomena are taken into account, in order to provide an application background. The theoretical framework is then adapted to a specific application, dealing with opinion formation dynamics, which leads to numerical simulations, that show some preliminary interesting results. The third paper,[5], further develops the theory introduced in the first and second papers, with the setting of a mathematical model, where external actions play a key role. The aim of [5] consists in showing the emergence of collective behaviors or macroscopic trends from interactions at the microscopic scale, where agents are grouped into functional subsystems. The approach is, again, based on the methods of the mathematical kinetic theory for active particles: in this application the specific functions expressed by the interacting entities are socio-political activities subjected to the influence of media. Also in this case, numerical simulations show a direct application of the theoretical model, by means of specific settings of key parameters of the model. Finally, the fourth paper,[6], derives an agent-based model, which allows the investigation of the socio-economic phenomenon of fashion. The model introduces two classes of agents, common agents and trend-setters, which play the dynamics that rule the emerging behaviors investigated by means of numerical
simulations. Both the numerical and analytical tools used in this last paper differentiate it from the previous three works. Nevertheless, except for some conceptual differences, the approach is still focused on extracting emerging behaviors from individual-based interactions. The goal is to illustrate and implement different methodologies within the same research environment.
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Kemahlioglu, Ziya Eda. "Formal Methods of Value Sharing in Supply Chains." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/4965.
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We consider a decentralized, two-echelon supply chain where the upper echelon --the supplier-- bears the inventory risk. To service the retailers, the supplier either keeps inventory reserved for each of her customers or else pools inventory to share among her customers. The common insight regarding inventory pooling is that it reduces costs and so increases profits for the supply chain party carrying inventory. However, it has recently been shown that inventory pooling may indeed reduce the total supply chain profits. We further show that inventory pooling may reduce supply chain profits even under traditional service contracts based on the frequently invoked measure of service, probability of stock-out.
We model the inventory transactions among the retailers and the supplier as a cooperative game. The players have the option of reserving inventory or forming inventory-pooling coalitions. The total profit of the coalitions is allotted to the players using a profit-sharing mechanism based on Shapley value. We analyze the properties of the proposed profit-sharing scheme in two steps. We first consider a stylized model with two retailers who are not necessarily identical. Then we extend the analysis to an arbitrary number of identical retailers. In both cases, we assume the demand across retailers is independent.
We find that the Shapley value allocations coordinate the supply chain and are individually rational. However for more than two retailers, they may not be in the core. Even when they satisfy all the stability properties, including membership in the core, they may be perceived unfair since a player's allocation can exceed his contribution to the total supply chain profit. In addition to analyzing the stability properties of the proposed allocation mechanism, we are also interested in the types of behavior the mechanism induces in the players. We find that the retailers prefer pooling partners with either very high or low service level requirements and the supplier prefers retailers with low service requirements since this gives her the ability to maximize her profit allocation. Finally, we analyze the effects of demand variance on the allocations and the profitability of strategic retailer coalitions.
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Mac, Dermed Liam Charles. "Value methods for efficiently solving stochastic games of complete and incomplete information." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50270.
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Multi-agent reinforcement learning (MARL) poses the same planning problem as traditional reinforcement learning (RL): What actions over time should an agent take in order to maximize its rewards? MARL tackles a challenging set of problems that can be better understood by modeling them as having a relatively simple environment but with complex dynamics attributed to the presence of other agents who are also attempting to maximize their rewards. A great wealth of research has developed around specific subsets of this problem, most notably when the rewards for each agent are either the same or directly opposite each other. However, there has been relatively little progress made for the general problem. This thesis address this lack.
Our goal is to tackle the most general, least restrictive class of MARL problems. These are general-sum, non-deterministic, infinite horizon, multi-agent sequential decision problems of complete and incomplete information. Towards this goal, we engage in two complementary endeavors: the creation of tractable models and the construction of efficient algorithms to solve these models. We tackle three well known models: stochastic games, decentralized partially observable Markov decision problems, and partially observable stochastic games. We also present a new fourth model, Markov games of incomplete information, to help solve the partially observable models.
For stochastic games and decentralized partially observable Markov decision problems, we develop novel and efficient value iteration algorithms to solve for game theoretic solutions. We empirically evaluate these algorithms on a range of problems, including well known benchmarks and show that our value iteration algorithms perform better than current policy iteration algorithms. Finally, we argue that our approach is easily extendable to new models and solution concepts, thus providing a foundation for a new class of multi-agent value iteration algorithms.
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Sprumont, Yves. "Three essays in collective choice theory." Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/40872.
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Calbert, Gregory. "Information, game theory and patch defence in the parasitic wasp Trissolcus basalis Wollaston (Hymenoptera : Scelionidae) /." Title page, contents and summary only, 1999. http://web4.library.adelaide.edu.au/theses/09PH/09phc143.pdf.
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Li, Xinxin. "Some operator splitting methods for convex optimization." HKBU Institutional Repository, 2014. https://repository.hkbu.edu.hk/etd_oa/43.
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Many applications arising in various areas can be well modeled as convex optimization models with separable objective functions and linear coupling constraints. Such areas include signal processing, image processing, statistical learning, wireless networks, etc. If these well-structured convex models are treated as generic models and their separable structures are ignored in algorithmic design, then it is hard to effectively exploit the favorable properties that the objective functions possibly have. Therefore, some operator splitting methods have regained much attention from different areas for solving convex optimization models with separable structures in different contexts. In this thesis, some new operator splitting methods are proposed for convex optimiza- tion models with separable structures. We first propose combining the alternating direction method of multiplier with the logarithmic-quadratic proximal regulariza- tion for a separable monotone variational inequality with positive orthant constraints and propose a new operator splitting method. Then, we propose a proximal version of the strictly contractive Peaceman-Rachford splitting method, which was recently proposed for the convex minimization model with linear constraints and an objective function in form of the sum of two functions without coupled variables. After that, an operator splitting method suitable for parallel computation is proposed for a convex model whose objective function is the sum of three functions. For the new algorithms, we establish their convergence and estimate their convergence rates measured by the iteration complexity. We also apply the new algorithms to solve some applications arising in the image processing area; and report some preliminary numerical results. Last, we will discuss a particular video processing application and propose a series of new models for background extraction in different scenarios; to which some of the new methods are applicable. Keywords: Convex optimization, Operator splitting method, Alternating direction method of multipliers, Peaceman-Rachford splitting method, Image processing
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Leleno, Joanna M. "A mathematical programming-based analysis of a two stage model of interacting producers." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/77818.
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This dissertation is concerned with the characterization, existence and computation of equilibrium solutions in a two-stage model of interacting producers. The model represents an industry involved with two major stages of production. On the production side there exist some (upstream) firms which perform the first stage of production and manufacture a semi-finished product, and there exist some other (downstream) firms which perform the second stage of production and convert this semi-finished product to a final commodity. There also exist some (vertically integrated) firms which handle the entire production process themselves.
In this research, the final commodity market is an oligopoly which may exhibit one of two possible behavioral patterns: follower-follower or multiple leader-follower. In both cases, the downstream firms are assumed to be price takers in purchasing the intermediate product. For the upstream stage, we consider two situations: a Cournot oligopoly or a perfectly competitive market.
An equilibrium analysis of the model is conducted with output quantities as decision variables. The defined equilibrium solutions employ an inverse derived demand function for the semi-finished product. This function is derived and characterized through the use of mathematical programming problems which represent the equilibrating process in the final commodity market. Based on this analysis, we provide sufficient conditions for the existence (and uniqueness) of an equilibrium solution, under various market assumptions. These conditions are formulated in terms of properties of the cost functions and the final product demand function.
Next, we propose some computational techniques for determining an equilibrium solution. The algorithms presented herein are based on structural properties of the inverse derived demand function and its local approximation. Both convex as well as nonconvex cases are considered.
We also investigate in detail the effects of various integrations among the producers on firms' profits, and on industry outputs and prices at equilibrium. This sensitivity analysis provides rich information and insights for industrial analysts and policy makers into how the foregoing quantities are effected by mergers and collusions and the entry or exit of various types of firms, as well as by differences in market behavior.Ph. D.
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Coulombe, Daniel. "Voluntary income increasing accounting changes : theory and further empirical investigation." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26983.
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This thesis presents a three step analysis of voluntary income increasing accounting changes. We first propose a theory as to why managers would elect to modify their reporting strategy. This theory builds on research on the economic factors motivating accounting choices, since it is assumed that accounting choices are a function of political costs, manager's compensation plans and debt constraints. Specifically, we claim that adversity motivates the manager to effect an income increasing accounting change.
Secondly, the thesis proposes a theoretical analysis of the potential market responses to a change announcement. The stock price effect of a change announcement is examined as a function of investors' rational anticipations of the manager's reporting actions and as a function of the level of information about adversity that investors may have prior to a change announcement.
An empirical analysis is presented in the third step of this thesis. Our empirical findings are that:
1- Change announcements, on average, have no significant impact on the market.
2- Relative to the Compustat population as a whole, firms that voluntarily adopt income increasing accounting changes exhibit symptoms of financial distress, suggesting that such change announcements are associated with financial adversity.
3- Firms which voluntarily adopt income increasing accounting changes tend to exhibit symptoms of financial distress one or more years prior to the change year, suggesting that change announcements tend not to be a timely source of information conveying distress to the market.
4- There is a significant negative association between investors' proxies for prior information about adversity and the market impact of the change, especially for the subset of firms with above average leverage, suggesting that the information content of the accounting change signal is inversely related to investors prior information about adversity.
The empirical results thus support the view that investors, at the time a change occurs, have information about the prevailing state of the world, and that they have rational anticipations with respect to the manager's reporting behavior. In this respect, the accounting change is, on average, an inconsequential signal that adds little to what investors already knew before the change announcement.Business, Sauder School of
Graduate
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Zhao, Kun. "Mathematical Methods for Network Analysis, Proteomics and Disease Prevention." Digital Archive @ GSU, 2012. http://digitalarchive.gsu.edu/math_diss/6.
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This dissertation aims at analyzing complex problems arising in the context of dynamical networks, proteomics, and disease prevention. First, a new graph-based method for proving global stability of synchronization in directed dynamical networks is developed. This method utilizes stability and graph theories to clarify the interplay between individual oscillator dynamics and network topology. Secondly, a graph-theoretical algorithm is proposed to predict Ca2+-binding site in proteins. The new algorithm enables us to identify previously-unknown Ca2+-binding sites, and deepens our understanding towards disease-related Ca2+-binding proteins at a molecular level. Finally, an optimization model and algorithm to solve a disease prevention problem are described at the population level. The new resource allocation model is designed to assist clinical managers to make decisions on identifying at-risk population groups, as well as selecting a screening and treatment strategy for chlamydia and gonorrhea patients under a fixed budget. The resource allocation model and algorithm can have a significant impact on real treatment strategy issues.
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Choy, Siu Kai. "Statistical histogram characterization and modeling : theory and applications." HKBU Institutional Repository, 2008. http://repository.hkbu.edu.hk/etd_ra/913.
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McKinley, Michael Scott. "Higher-order boundary condition perturbation methods in transport and diffusion theory." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/16034.
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Maslar, David Wang X. H. Tsoi Allanus Hak-Man. "An experimental study of the game of Nim." Diss., Columbia, Mo. : University of Missouri-Columbia, 2009. http://hdl.handle.net/10355/6725.
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The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Title from PDF of title page (University of Missouri--Columbia, viewed on March 23, 2010). Thesis advisors: Dr. X. H. Wang and Dr. Allanus Tsoi. Includes bibliographical references.
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Lipowski, Miroslav. "Organizing police expeditionary capacities insights into a wicked problem territory with mathematical modeling /." Thesis, Monterey, California : Naval Postgraduate School, 2010. http://edocs.nps.edu/npspubs/scholarly/theses/2010/Jun/10Jun%5FLipowski.pdf.
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Thesis (M.S. in Defense Analysis)--Naval Postgraduate School, June 2010.Thesis Advisor(s): Jansen, Erik ; Second Reader: Giordano, Frank. "June 2010." Description based on title screen as viewed on July 15, 2010. Author(s) subject terms: Police expeditionary capacities; counterinsurgency; gendarmeries; paramilitary organizations; executive policing; population centric operations; mathematical modeling; game theory; interagency cooperation; stabilization and reconstruction operations; irregular warfare; security force assistance. Includes bibliographical references (p. 57-58). Also available in print.
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Steinle, Peter John. "Finite difference methods for the advection equation /." Title page, table of contents and abstract only, 1993. http://web4.library.adelaide.edu.au/theses/09PH/09phs8224.pdf.
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Zhu, Huaiyu. "Neural networks and adaptive computers : theory and methods of stochastic adaptive computation." Thesis, University of Liverpool, 1993. http://eprints.aston.ac.uk/365/.
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This thesis studies the theory of stochastic adaptive computation based on neural networks. A mathematical theory of computation is developed in the framework of information geometry, which generalises Turing machine (TM) computation in three aspects - It can be continuous, stochastic and adaptive - and retains the TM computation as a subclass called "data processing". The concepts of Boltzmann distribution, Gibbs sampler and simulated annealing are formally defined and their interrelationships are studied. The concept of "trainable information processor" (TIP) - parameterised stochastic mapping with a rule to change the parameters - is introduced as an abstraction of neural network models. A mathematical theory of the class of homogeneous semilinear neural networks is developed, which includes most of the commonly studied NN models such as back propagation NN, Boltzmann machine and Hopfield net, and a general scheme is developed to classify the structures, dynamics and learning rules. All the previously known general learning rules are based on gradient following (GF), which are susceptible to local optima in weight space. Contrary to the widely held belief that this is rarely a problem in practice, numerical experiments show that for most non-trivial learning tasks GF learning never converges to a global optimum. To overcome the local optima, simulated annealing is introduced into the learning rule, so that the network retains adequate amount of "global search" in the learning process. Extensive numerical experiments confirm that the network always converges to a global optimum in the weight space. The resulting learning rule is also easier to be implemented and more biologically plausible than back propagation and Boltzmann machine learning rules: Only a scalar needs to be back-propagated for the whole network. Various connectionist models have been proposed in the literature for solving various instances of problems, without a general method by which their merits can be combined. Instead of proposing yet another model, we try to build a modular structure in which each module is basically a TIP. As an extension of simulated annealing to temporal problems, we generalise the theory of dynamic programming and Markov decision process to allow adaptive learning, resulting in a computational system called a "basic adaptive computer", which has the advantage over earlier reinforcement learning systems, such as Sutton's "Dyna", in that it can adapt in a combinatorial environment and still converge to a global optimum. The theories are developed with a universal normalisation scheme for all the learning parameters so that the learning system can be built without prior knowledge of the problems it is to solve.
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Ellis, Eric. "Productive play| Exploring participant motivations of a modding community surrounding a massively multiplayer online game." Thesis, Pepperdine University, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3667191.
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The phenomenon of user-generated content and modification for video games, known as modding, is increasingly common, but why individuals are motivated to engage in significant work for no pay is still poorly understood. Drawing upon the Communities of Practice theories proposed by Jean Lave and Ettienne Wenger, this paper explored the similarities and differences between a community of addon software developers for Blizzard Entertainment's popular Massively Multiplayer Online Game, World of Warcraft, and other Free/Open Source Software communities. Through a series of ethnographic interviews, and an online survey of addon developers, research found the addon development community describes itself primarily as devoted game players rather than software developers, motivated primarily by a desire to fill personal in-game needs, and only later, by the more unclear rewards of contributing to the Community of Practice surrounding addon development.
Similarly, though addon developers have a strong affinity with many practices and attitudes toward intellectual property espoused by F/OSS communities, they have ultimately coalesced around shared practices which encourage and honor individual ownership of intellectual property, rather than more "free" distribution models. Considering these findings, a new understanding emerges for a specific type of Community of Practice, termed a Community of Passion, that allows future research to more clearly identify and describe a playful and passionate approach to productive activity increasingly seen not only in online gaming communities, but also in other settings such as the emergent Maker communities where creativity and democratized production are valued.
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Schwartz, Alexandra [Verfasser], and Christian [Akademischer Betreuer] Kanzow. "Mathematical Programs with Complementarity Constraints : Theory, Methods and Applications / Alexandra Schwartz. Betreuer: Christian Kanzow." Würzburg : Universitätsbibliothek der Universität Würzburg, 2011. http://d-nb.info/1014891930/34.
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Oladi, Gholamreza. "Three essays in international economics." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=36784.
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In international economics literature, different variants of the Nash equilibrium have been used to formulate strategic and retaliative behavior. However, the negotiation process underlying the Nash equilibrium does not capture the notion of retaliation properly. We use the "contingent threat situation" (Greenberg, 1990) to reformulate three different international economic environments.First, a two-country, two-commodity model of trade is considered to reformulate the tariff retaliations. It is known that tariff retaliations lead to a Nash equilibrium outcome, a non-free trade outcome. We show, in the framework of the "theory of social situations", that the free trade equilibrium is supported by a "stable standard of behavior".
Second, the basic two-country, single commodity model is employed to formulate the interactive and retaliatory policies regarding the choice between foreign investment and immigration. Considering three different strategic environments, we investigate the outcomes supported by "stable standards of behavior" under these strategic scenarios. We also provide a critical examination of Jones-Coelho-Easton's proposition (Jones, Coelho, and Easton, 1986).
Third, a simple model of international debt is formulated using a strategic form game. In the game, a country in financial crisis and on the verge of default is requesting a new loan, and a bank, with exposure to the foreign country's debt, contemplates whether it should issue the new loan. We show that "issue a new loan" and "not default", a Pareto optimum pair of strategies, is stable. Interestingly, we get this result by using a non-cooperative negotiation process, offered by the "individual contingent threat situation".
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Riposo, Julien. "Computational and Mathematical Methods for Data Analysis in Biology and Finance." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066177/document.
Full textAbstract:
Les mathématiques sont comprises en tant qu’ensemble d’idées abstraites, dans le sens où le monde réel – ou plutôt réalité – n’a pas à intervenir. Pourtant, certains faits mathématiques observables dans des données expérimentales ou simulées peuvent être contre-intuitifs. La thèse est divisée en deux parties : premièrement, on étudie mathématiquement les matrices du genre celles dont nous avons discutées en biologie et finance. En particulier, nous mettons en évidence le fait contre-intuitif suivant : pour ces matrices, le vecteur propre associé à la plus haute valeur propre est très proche de la somme de chacune des lignes de la matrice, colonne par colonne. Nous discutons aussi d’applications en théorie des graphes avec bon nombre de simulations numériques. Dans un second temps, nous attaquons le problème des contacts géniques : à partir d’une carte de contact génique, un vrai défi actuel est de retrouver la structure tridimensionnelle de l’ADN. Nous proposons diverses méthodes d’analyse matricielle de données, dont une met en évidence l’existence, dans le noyau, de zones disjointes où les interactions sont de différents types. Ces zones sont des compartiments nucléaires. Avec d’autres données biologiques, nous mettons en évidence la fonction biologique de chacun de ces compartiments. Les outils d’analyses sont ceux utilisés en finance pour analyser des matrices d’auto-corrélation, ou même des séries temporellesMathematics are understood as a set of abstract ideas, in the measure of the real world – or reality – has no way to intervene. However, some observable mathematical facts in experimental or simulated data can be counter-intuitive. The PhD is divided into two parts: first, we mathematically study the matrices of the same type of the ones in biology and finance. In particular, we show the following counter-intuitive fact: for these matrices, the eigenvector associated with the highest eigenvalue is close to the sum of each row, column by column. We also discuss some applications to graph theory with many numerical simulations and data analysis.On the other hand, we will face the genetic contact problem: from a contact map, a real current challenge is to find the DNA 3D-structure. We propose several matrix analysis methods, which one show disjoinct areas in the nucleus where the DNA interactions are different. These areas are nuclear compartments. With other biological features, we characterize the biological function of each of the compartments. The analysis tools are the ones already used in finance to analyze the autocorrelation matrices, or even time series
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Zhu, Dongming 1963. "Asymmetric heavy-tailed distributions : theory and applications to finance and risk management." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=102854.
Full textAbstract:
This thesis focuses on construction, properties and estimation of asymmetric heavy-tailed distributions, as well as on their applications to financial modeling and risk measurement. First of all, we suggest a general procedure to construct a fully asymmetric distribution based on a symmetrically parametric distribution, and establish some natural relationships between the symmetric and asymmetric distributions. Then, three new classes of asymmetric distributions are proposed by using the procedure: the Asymmetric Exponential Power Distributions (AEPD), the Asymmetric Student-t Distributions (ASTD) and the Asymmetric Generalized t Distribution (AGTD). For the first two distributions, we give an interpretation of their parameters and explore basic properties of them, including moments, expected shortfall, characterization by the maximum entropy property, and the stochastic representation. Although neither distribution satisfies the regularity conditions under which the ML estimators have the usual asymptotics, due to a non-differentiable likelihood function, we nonetheless establish asymptotics for the full MLE of the parameters. A closed-form expression for the Fisher information matrix is derived, and Monte Carlo studies are provided. We also illustrate the usefulness of the GARCH-type models with the AEPD and ASTD innovations in the context of predicting downside market risk of financial assets and demonstrate their superiority over skew-normal and skew-Student's t GARCH models. Finally, two new classes of generalized extreme value distributions, which include Jenkinson's GEV (Generalized Extreme Value) distribution (Jenkinson, 1955) as special cases, are proposed by using the maximum entropy principle, and their properties are investigated in detail.
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CHESSA, MICHELA. "A MATHEMATICAL ANALYSIS OF CONFLICTS IN VOTING SYSTEMS." Doctoral thesis, Università degli Studi di Milano, 2013. http://hdl.handle.net/2434/217565.
Full textAbstract:
Game Theory applied to voting gives rise to the study of many different topics. In this thesis we present some results in order to evaluate the power share inside a Parliament, to analyze the criteria for the assessment of the voters’ preferences and to provide more efficient ways to compute the existing instruments.
The first part of the thesis deals with the issue of power in a voting system. In order to better analyze it, we investigate the way of combining a communication structure with the already existing indices of power. Moreover, we present the possibility of assuming some coalitions as less probable, but not infeasible, as the political scenario is complex enough to admit the possibility of very unlikely coalitions to form. Then, we add another important aspect to the problem; the alliances inside a decisional situation are not stable, but may evolve with time, mainly due to the fact that each agent aims at getting a higher power. We refer to an already existing instrument which, theoretically, may perfectly describe this situation. Unfortunately, the current computational complexity does not permit to adopt it in many real cases. Another important topic is the evaluation of the power to block instead of the power to win. We provide an index which evaluates the veto power and which can be extended in order to catch other characteristics of the game; for example, the probability that a party takes a particular decision, or that not every member of a party is present at the vote.
The second part of this thesis considers a previous step of the formation of a democracy: the evaluation of how much the resulting Parliament reflects the preferences expressed by the electors. We think that the goodness of a Parliament mainly depends on the power share between the parties and not only on the number of seats.
Finally, the last part shows a new exact method to improve the efficiency of the evaluation of one of the existing indices of power, the Public Good index.
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"Agent-based models of complex adaptive systems." 2000. http://library.cuhk.edu.hk/record=b5890318.
Full textAbstract:
by Lo Ting Shek = 複雜適應系統中的個體為本模型 / 盧庭碩.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.
Includes bibliographical references (leaves 105-107).
Text in English; abstracts in English and Chinese.
by Lo Ting Shek = Fu za shi ying xi tong zhong de ge ti wei ben mo xing / Lu Tingshuo.
Chapter 1 --- Introduction --- p.1
Chapter 2 --- Minority game --- p.9
Chapter 2.1 --- The model --- p.9
Chapter 2.2 --- Review on selected work on MG --- p.13
Chapter 2.2.1 --- Market efficiency and Phase transition --- p.13
Chapter 2.2.2 --- Crowd effect in MG --- p.17
Chapter 2.2.3 --- Hamming distance between strategies --- p.19
Chapter 2.2.4 --- Statistical mechanics of systems with heterogeneous agents --- p.21
Chapter 3 --- Theory of the minority game --- p.23
Chapter 3.1 --- Formalism --- p.23
Chapter 3.2 --- Discussion --- p.31
Chapter 4 --- Evolutionary Minority Game --- p.33
Chapter 4.1 --- Model --- p.33
Chapter 4.2 --- Results --- p.36
Chapter 4.3 --- Discussion --- p.38
Chapter 5 --- Theory of the Evolutionary Minority game --- p.43
Chapter 5.1 --- The theory of D'hulst and Rodgers [1] --- p.44
Chapter 5.1.1 --- Discussion on the D'hulst and Rodgers's theory --- p.51
Chapter 5.2 --- Theory of EMG [2] --- p.54
Chapter 5.2.1 --- Formalism --- p.55
Chapter 5.2.2 --- Results --- p.60
Chapter 5.2.3 --- Discussion --- p.66
Chapter 6 --- Evolutionary Minority Game with arbitrary cutoffs --- p.68
Chapter 6.1 --- Model --- p.68
Chapter 6.2 --- Results --- p.69
Chapter 6.3 --- Theory --- p.76
Chapter 6.4 --- Discussion --- p.85
Chapter 7 --- Evolutionary minority game with heterogeneous strategy distribution --- p.88
Chapter 7.1 --- Model --- p.89
Chapter 7.2 --- Results --- p.90
Chapter 7.3 --- Discussion --- p.99
Chapter 8 --- Conclusion --- p.103
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KIRYSHEVA, Irina. "Essays in applied game theory." Doctoral thesis, 2015. http://hdl.handle.net/1814/35439.
Full textAbstract:
Defence date: 23 March 2015Examining Board: Professor Fernando Vega-Redondo, Supervisor, Bocconi University; Professor Piero Gottardi, EUI; Professor Paolo Pin, Università degli Studi di Siena; Professor Giovanni Ponti, Universidad de Alicante.
My thesis covers different aspects of applied game theory. The first paper looks at a two-sided asymmetric information game where agents make a collaborative decision not knowing each others' types. In the model, an intermediary has full knowledge about the types of agents and can make a decision that brings information to some types. However, once he puts the information on the table the agents are not obliged to pay him, which undermines his incentive to participate in the first place. I find that, nevertheless, the intermediary is still welfare-improving. In my second chapter I search for the optimal prize schemes in contests with sabotage. In the presence of sabotage, a standard prize scheme where all of the prize is given to the winner is no longer optimal as it creates very high incentives for sabotage. I show that in that case, an optimal prize structure may also assume a positive reward for contestants that are behind. With a higher number of contestants sabotage becomes a public good and therefore it is a lesser concern for the designer. In that case, when sabotage is expensive, the designer can achieve the first best by giving the whole sum to the winner. When I extend the problem to the continuous case the solution crucially depends on the cost of sabotage. When sabotage is expensive, the principal wants to give all of the prize to the winner, while when it is cheap he does not want to make a contest at all, and distributes all prizes equally. In the third paper we analyze to what extent knowing game theory alters a persons' behavior. Our experiment showed a huge difference in results before and after the course. However results suggest that players behave less cooperatively not because of the knowledge of game theory per se, but due to changed expectations. We have also found that a course on game theory increases the level of reasoning.