Liu, Weiyang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 111-113). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction and Literature Review --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.1.1 --- Background and Motivating examples --- p.2 / Chapter 1.1.2 --- Basic Concepts --- p.4 / Chapter 1.1.3 --- Outline of the thesis --- p.6 / Chapter 1.2 --- Literature Review --- p.8 / Chapter 2 --- Multi-period Cooperative Re-investment Games: The Basic Model --- p.11 / Chapter 2.1 --- Basic settings and assumptions --- p.11 / Chapter 2.2 --- The problem --- p.13 / Chapter 3 --- Three sub-models and the allocation rule of Sub-Model III --- p.17 / Chapter 3.1 --- Three possible sub-models of the basic model --- p.17 / Chapter 3.1.1 --- Sub-model I --- p.17 / Chapter 3.1.2 --- Sub-model II --- p.18 / Chapter 3.1.3 --- Sub-model III --- p.19 / Chapter 3.2 --- The allocation rule of Sub-model III --- p.19 / Chapter 4 --- A two period example of the revised basic model --- p.25 / Chapter 4.1 --- The two period example with two projects --- p.25 / Chapter 4.2 --- The algorithm for the dual problem --- p.29 / Chapter 5 --- Extensions of the Basic Model --- p.35 / Chapter 5.1 --- The model with stochastic budgets --- p.36 / Chapter 5.2 --- The core of the model with stochastic budgets --- p.39 / Chapter 5.3 --- An example: the two-period case of models with stochastic bud- gets and an algorithm for the dual problem --- p.46 / Chapter 5.4 --- An interesting marginal effect --- p.52 / Chapter 5.5 --- "A Model with stochastic project prices, stochastic returns and stochastic budgets" --- p.54 / Chapter 6 --- Multi-period Re-investment Model with risks --- p.58 / Chapter 6.1 --- The Model with l1 risk measure --- p.58 / Chapter 6.2 --- The Model with risk measure --- p.66 / Chapter 7 --- Numerical Tests --- p.70 / Chapter 7.1 --- The affects from uncertainty changes --- p.71 / Chapter 7.2 --- The affects from budget changes --- p.71 / Chapter 7.3 --- The affects from the budget changes of only one group --- p.71 / Chapter 8 --- Conclusive Remarks --- p.77 / Chapter A --- Original Data and Analysis for Section 7.1 (Partial) --- p.79 / Chapter B --- Data Analysis for Section 7.2 (Partial) --- p.95 / Chapter C --- Data Analysis for Section 7.3 (Partial) --- p.98

Lee, Kwan Ho = 探討網絡上的若干動態過程 / 李鈞浩. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 114-118). / Abstracts in English and Chinese. / Lee, Kwan Ho = Tan tao wang luo shang de ruo gan dong tai guo cheng / Li Junhao. / Chapter 1 --- Overview --- p.1 / Chapter 2 --- Networks --- p.5 / Chapter 2.1 --- Describing Networks --- p.5 / Chapter 2.1.1 --- Adjacency Matrix --- p.6 / Chapter 2.1.2 --- "Degree, Degree Distribution and Mean Degree" --- p.6 / Chapter 2.1.3 --- Clustering Coefficient --- p.7 / Chapter 2.1.4 --- "Shortest Path, Shortest Distance and Diameter" --- p.7 / Chapter 2.1.5 --- Betweenness --- p.9 / Chapter 2.2 --- Barabasi-Albert (BA) Network --- p.10 / Chapter 2.2.1 --- Construction of BA Network --- p.10 / Chapter 2.2.2 --- Analytical Study of Degree Distribution --- p.11 / Chapter 2.2.3 --- Numerical Study of Degree Distribution --- p.12 / Chapter 2.2.4 --- Shortest Distance --- p.13 / Chapter 2.3 --- Summary --- p.14 / Chapter 3 --- Routing in Networks: A Review --- p.16 / Chapter 3.1 --- Introduction --- p.16 / Chapter 3.2 --- Dijkstra´ةs Algorithm --- p.17 / Chapter 3.2.1 --- Algorithm --- p.17 / Chapter 3.2.2 --- Running Time --- p.18 / Chapter 3.2.3 --- Routing Table Based on Shortest Path Algorithm --- p.19 / Chapter 3.3 --- Routing Model --- p.19 / Chapter 3.3.1 --- General Setup --- p.19 / Chapter 3.3.2 --- Phase Transition and Evaluation of Network Performance --- p.20 / Chapter 3.4 --- Using Shortest Path as Routing Algorithm on BA Networks --- p.21 / Chapter 3.5 --- Other Routing Algorithms --- p.22 / Chapter 3.5.1 --- Efficient Path --- p.23 / Chapter 3.5.2 --- Routing based on Local Structural Information --- p.24 / Chapter 3.5.3 --- Routing based on Dynamical Information --- p.25 / Chapter 3.6 --- Summary --- p.26 / Chapter 4 --- Optimization of Routing Efficiency through Redistributing Limited Resources --- p.28 / Chapter 4.1 --- A Reallocation Rule - Short to Long (S2L) --- p.29 / Chapter 4.2 --- Performance Enhancement After Applying S2L --- p.33 / Chapter 4.3 --- Optimized Capability Distribution in Detail --- p.36 / Chapter 4.4 --- Summary --- p.44 / Chapter 5 --- N-person Evolutionary Snowdrift Game: A Review --- p.47 / Chapter 5.1 --- Snowdrift Game (SG) and Evolutionary Snowdrift Game (ESG) --- p.47 / Chapter 5.2 --- N-person Evolutionary Snowdrift Game --- p.49 / Chapter 5.2.1 --- Payoffs of C-character and D-character Agents --- p.49 / Chapter 5.2.2 --- Replicator Dynamics --- p.50 / Chapter 5.2.3 --- Numerical Simulations --- p.52 / Chapter 5.3 --- Summary --- p.55 / Chapter 6 --- NESG on Complex Network --- p.56 / Chapter 6.1 --- Models --- p.57 / Chapter 6.2 --- Results of Model A (varying N) --- p.58 / Chapter 6.2.1 --- Correlation of Characters in Degree --- p.60 / Chapter 6.2.2 --- Correlation of Characters in Distance --- p.62 / Chapter 6.3 --- Results of Model B (Fixed-N) --- p.63 / Chapter 6.3.1 --- Correlation of Characters in Degree --- p.64 / Chapter 6.4 --- Summary --- p.69 / Chapter 7 --- Synchronization: A Review --- p.71 / Chapter 7.1 --- Kuramoto Model --- p.72 / Chapter 7.1.1 --- Analytical Method --- p.74 / Chapter 7.1.2 --- Numerical Method --- p.78 / Chapter 7.1.3 --- Summary of Kuramoto Model --- p.81 / Chapter 7.2 --- Integrate-and-Fire Model --- p.81 / Chapter 8 --- Kuramoto Model with Spatially Distributed Oscillators --- p.84 / Chapter 8.1 --- Model --- p.84 / Chapter 8.2 --- Numerical Results --- p.85 / Chapter 8.3 --- Analytic Results --- p.87 / Chapter 8.4 --- Summary --- p.90 / Chapter 9 --- Integrate-Fire-and-Run Model --- p.92 / Chapter 9.1 --- Model --- p.92 / Chapter 9.2 --- Two-Body System --- p.94 / Chapter 9.2.1 --- Case I: Oscillators A and B are in different sites --- p.94 / Chapter 9.2.2 --- Case II: Oscillators A and B are in the same site --- p.101 / Chapter 9.2.3 --- Comparison of Analytic Results and Numerical Simulations of Two-Body system --- p.103 / Chapter 9.3 --- N-Body System --- p.105 / Chapter 9.4 --- Summary --- p.111 / Chapter 10 --- Outlook --- p.112 / Bibliography --- p.114

Real estate activity is notably influenced by local land use regulation. By acting as redtape costs or explicitly through compensatory payments, such rules typically increase construction costs by reducing supply and increasing demand in the housing market, which leads to higher prices. This is the first study to model the decision-making process of housing supply using a game theoretic approach. To shed light on the roleof regulation and competition in this industry, I employ a static-entry model that incorporates the demand, cost and strategic factors common to the activity. I built aunique data set forthe city of São Paulo, Brazil, with information on the universe ofnew residential buildings launched in the city, along with a history of all licenses requested by the developers tothe government for each project. My empirical results show that the regulation play akey role in developer activity. For the areas with the most intense activity of the city,the bureaucracy in the residential approval process cost annually R$ 47 millions (US$ 14millions) by entrant firm. / A atividade imobiliária é particularmente influenciada pela regulação do uso da terra. Ao agir como \"custos burocráticos\" ou explicitamente por meio de pagamentos compensatórios,essas regras normalmente aumentam os custos de construção ao reduzir a oferta e aumentara demanda de novas residências, o que leva a preços mais altos. Este é o primeiro estudo amodelar o processo de decisão de oferta de residências usando uma abordagem de teoria dos jogos. Para mostrar os efeitos da regulação e da competição nesse setor, eu emprego um modelo de entrada estático que incorpora os fatores de demanda, custo e estratégicos comuns a essa atividade. Eu construí uma base de dados única para a cidade de São Paulo, Brasil, com informações sobre o universo de novos empreendimentos residenciais na cidade, juntamente comum histórico de todas as licenças e alvarás requeridos pelas incorporadoras à Prefeitura para cada projeto. Meus resultados mostram que a regulação tem um papel chave na atividade imobiliária. Para as áreas com atividade mais intensa da cidade, a burocracia no processo de aprovação de novas residências tem um custo média anual de R$ 47 milhões por firma entrante no mercado.

In this paper I introduce some background for subtraction games and explore the Sprague-Grundy functions defined on them. I exhibit some subtraction games where the functions are guaranteed to be strictly periodic. I also exhibit a class of subtraction games which have bounded range, and show there are uncountably many of these.

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The Backward Induction strategy for the Centipede Game leads us to a counterfactual reasoning paradox, The Centipede Game paradox. The counterfactual reasoning proving the backward induction strategy for the game appears to rely on the players in the game not choosing that very same backward induction strategy. The paradox is a general paradox that applies to backward induction reasoning in sequential, perfect information games. Therefore, the paradox is not only problematic for the Centipede Game, but it also affects counterfactual reasoning solutions in games similar to the Centipede Game. The Centipede Game is a prime illustration of this paradox in counterfactual reasoning. As a result, this paper will use a material versus subjunctive/counterfactual conditional analysis to provide a theoretical resolution to the Centipede Game, with the hope that a similar solution can be applied to other areas where this paradox may appear. The solution involves delineating between the epistemic systems of the players and the game theorists.

Le cloud computing est l’accomplissement du rêve de nombreux informaticiens désireux de transformer et d’utiliser leurs logiciels comme de simples services, rendant ces derniers plus attractifs et séduisants pour les utilisateurs. Dans le cadre de cette thèse, les technologies du cloud computing sont présentées, ainsi que les principaux défis que ce dernier va rencontrer dans un futur proche, notamment pour la gestion et l’analyse des données. A partir de la théorie moderne d'ordonnancements des tâches, nous avons proposé une gestion hiérarchique d’ordonnancements des tâches qui satisfait aux différentes demandes des cloud services. D’un point de vue théorique, nous avons principalement répondu à trois questions cruciales de recherche. Premièrement, nous avons résolu le problème de l'allocation des ressources au niveau de l’utilisateur. Nous avons en particulier proposé des algorithmes basés sur la théorie des jeux. Avec une méthode Bayésienne d’apprentissage, l'allocation des ressources atteint l'équilibre de Nash parmi les utilisateurs en compétition malgré une connaissance insuffisante des comportements de ces derniers. Deuxièmement, nous avons abordé le problème d'ordonnancements des tâches au niveau du système. Nous avons trouvé un nouveau seuil pour l'utilisation d’ordonnancements des tâches en ligne, considérant le dispositif séquentiel de MapReduce. Ce seuil donne de meilleurs résultats que les méthodes existantes dans l’industrie. Troisièmement, nous avons défini un critère de comparaison pour les tests d’ordonnancements de tâches en ligne. Nous avons proposé un concept de fiabilité d'essai pour évaluer la probabilité qu'un ensemble de tâches aléatoires passe un essai donné. Plus la probabilité est grande, plus la fiabilité est élevée. Un test présentant une grande fiabilité garantit une bonne utilisation du système. D’un point de vue pratique, nous avons développé un simulateur basé sur le concept de MapReduce. Ce simulateur offre un environnement directement utilisable par les chercheurs familiers avec SimMapReduce, leur permettant de s’affranchir des aspects informatiques d’implémentations et leur permettant notamment de se concentrer sur les aspects algorithmiques d’un point de vue théorique. / Cloud computing, the long-held dream of computing as a utility, has the potential to transform a large part of the IT industry, making software even more attractive as a service and shaping the way in which hardware is designed and purchased. In this thesis, we reviewed the new cloud computing technologies, and indicated the main challenges for their development in future, among which resource management problem stands out and attracts our attention. Combining the current scheduling theories, we proposed cloud scheduling hierarchy to deal with different requirements of cloud services. From the theoretical aspects, we have accomplished three main research issues. Firstly, we solved the resource allocation problem in the user-level of cloud scheduling. We proposed game theoretical algorithms for user bidding and auctioneer pricing. With Bayesian learning prediction, resource allocation can reach Nash equilibrium among non-cooperative users even though common knowledge is insufficient. Secondly, we addressed the task scheduling problem in the system-level of cloud scheduling. We proved a new utilization bound for on-line schedulability test, considering the sequential feature of MapReduce. We deduced the relationship between cluster utilization bound and the ratio of Map to Reduce. This new schedulable bound with segmentation uplifts classic bound which is most used in industry. Thirdly, we settled the comparison problem among on-line schedulability tests in cloud computing. We proposed a concept of test reliability to evaluate the probability that a random task set could pass a given schedulability test. The larger the probability is, the more reliable the test is. From the aspect of system, a test with high reliability can guarantee high system utilization. From the practical aspects, we have developed a simulator to model MapReduce framework. This simulator offers a simulated environment directly used by MapReduce theoretical researchers. The users of SimMapReduce only concentrate on specific research issues without getting concerned about finer implementation details for diverse service models, so that they can accelerate study progress of new cloud technologies.

Heterogeneous Computing (HC) systems achieve high performance by networking together computing resources of diverse nature. The issues of task assignment and scheduling are critical in the design and performance of such systems. In this thesis, an auction based game theoretic framework is developed for dynamic task scheduling in HC systems. Based on the proposed game theoretic model, a new dynamic scheduling algorithm is developed that uses auction based strategies. The dynamic scheduling algorithm yields schedules with shorter completion times than static schedulers while incurring higher scheduling overhead. Thus, a second scheduling algorithm is proposed which uses an initial schedule generated with a learning automaton based algorithm, and then heuristics are used to identify windows of tasks within the application that can be rescheduled dynamically during run time.

The optimal allocation of the resources to the emergency locations in the event of multiple crises in an urban environment is an intricate problem, especially when the available resources are limited. In such a scenario, it is important to allocate emergency response units in a fair manner based on the criticality of the crisis events and their requests. In this research, a crisis management tool is developed which incorporates a resource allocation algorithm. The problem is formulated as a game theoretic framework in which the crisis events are modeled as the players, the emergency response centers as the resource locations with emergency units to be scheduled and the possible allocations as strategies. The pay-off is modeled as a function of the criticality of the event and the anticipated response times. The game is played assuming a specific region within a certain locality of the crisis event to derive an optimal allocation. If a solution is not feasible, the perimeter of the locality in consideration is increased and the game is repeated until convergence. Experimental results are presented to illustrate the efficacy of the proposed methodology and metrics are derived to quantify the fairness of the solution. A regression analysis has been performed to identify the statistical significance of the results.

The problem of resource allocation and management in the context of multiple crises occurring in an urban environment is challenging. In this thesis, the problem is formulated using game theory and a solution is developed based on the Nash equilibrium to optimize the allocation of resources to the different crisis events in a fair manner considering several constraints such as the availability of resources, the criticality of the events, the amount of resources requested etc. The proposed approach is targeted at managing small to medium level crisis events occurring simultaneously within a specific pre-defined perimeter with the resource allocation centers being located within the same fixed region. The objective is to maximize the utilization of the emergency response units while minimizing the response times. In the proposed model, players represent the crisis events and the strategies correspond to possible allocations. The choice of strategies by each player impacts the decisions of the other players. The Nash equilibrium condition will correspond to the set of strategies chosen by all the players such that the resource allocation optimal for a given player also corresponds to the optimal allocations of the other players. The implementation of the Nash equilibrium condition is based on the Hansen's combinatorial theorem based approximation algorithm. The proposed solution has been implemented using C++ and experimental results are presented for various test cases. Further, metrics are developed for establishing the quality and fairness of the obtained results.