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.

This dissertation studies multi-agent algorithms for learning Nash equilibrium strategies in games with many players. We focus our study on a set of learning dynamics in which agents seek to myopically optimize their next-stage utility given some forecast of opponent behavior; i.e., players act according to myopic best response dynamics. The prototypical algorithm in this class is the well-known fictitious play (FP) algorithm. FP dynamics are intuitively simple and can be seen as the \natural" learning dynamics associated with the Nash equilibrium concept. Accordingly, FP has received extensive study over the years and has been used in a variety of applications. Our contributions may be divided into two main research areas. First, we study fundamental properties of myopic best response (MBR) dynamics in large-scale games. We have three main contributions in this area. (i) We characterize the robustness of MBR dynamics to a class of perturbations common in real-world applications. (ii) We study FP dynamics in the important class of large-scale games known as potential games. We show that for almost all potential games and for almost all initial conditions, FP converges to a pure-strategy (deterministic) equilibrium. (iii) We develop tools to characterize the rate of convergence of MBR algorithms in potential games. In particular, we show that the rate of convergence of FP is \almost always" exponential in potential games. Our second research focus concerns implementation of MBR learning dynamics in large-scale games. MBR dynamics can be shown, theoretically, to converge to equilibrium strategies in important classes of large-scale games (e.g., potential games). However, despite theoretical convergence guarantees, MBR dynamics can be extremely impractical to implement in large games due to demanding requirements in terms of computational capacity, information overhead, communication infrastructure, and global synchronization. Using the aforementioned robustness result, we study practical methods to mitigate each of these issues. We place a special emphasis on studying algorithms that may be implemented in a network-based setting, i.e., a setting in which inter-agent communication is restricted to a (possibly sparse) overlaid communication graph. Within the network-based setting, we also study the use of so-called \inertia" in MBR algorithms as a tool for learning pure-strategy NE.

Evolutionary game theory tries to explain the emergence of stable behaviors observed in human and animal societies. Prominent examples of such behaviors are cooperative and conformist behaviors. In the first part of the thesis, we develop a model of indirect reciprocity with institutional screening to study how institutions may promote cooperative behavior. We show that cooperation can emerge if screening institutions are sufficiently reliable at identifying cooperators. The second part presents a large-population learning model in which individuals update their beliefs through time. In the model, only one individual updates his beliefs each period. We show that a population, playing a game with two strategies, eventually learns to play a Nash equilibrium. We focus on coordination games and prove that a unique behavior arises both when players use myopic and perturbed best replies. The third part studies the payoff calculation in an evolutionary setting. By introducing mutual consent as a requirement for game play, we provide a more realistic alternative way to compute payoffs. / <p>At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Manuscript. Paper 3: Manuscript.</p>

How life originated from physical and chemical processes is one of the great questions still unanswered today. Studies towards this effort have transitioned from the notion of a single self-replicating entity to the idea that a network of interacting molecules made this initial biological leap. In order to understand the chemical kinetic and thermodynamic mechanisms that could engender pre-life type networks we present an empirical characterization of a network of RNA recombinase molecules. We begin with 1-, 2-, and 3-molecular ensembles and provide a game theoretic analysis to describe the frequency dependent dynamics of competing and cooperating RNA genotypes. This is then extended to 4- and 5-membered networks where varying topologies are compared and mechanisms that could lead to preferential growth and selection of genotypes are described. At the core of these network connections is ribozyme catalysis initiated through a 3-nucleotide base-pairing interface. With the development of a fluorescence anisotropy method, we are able to illustrate a correlation between these binding thermodynamics and network outcomes. Finally, we consider how the heterogeneity of the environment could impact network dynamics and develop a spectrum of spatial inducing methods in which our chemical populations can be probed. These experiments illustrate simple chemical dynamics of RNA interactions, yet these very processes are the foundation for building complexity and ultimately from where selection and evolvability derive.

<p>Population growth and increasing life standards contributed to a high demand for food worldwide. Simultaneously, there is growing evidence that more food is being lost or wasted through the different stages of the supply chain. In the developed world, including the United States, consumer waste often constitutes more than 60% of all food losses. </p> This dissertation explores the problem of consumer waste from three different perspectives. In the first essay, a game-theoretic model of a direct interaction between consumers and a retailer with monopoly power is developed to capture the effects of dynamic pricing on the transfer of perishable inventory to consumers. The retailer chooses its optimal price taking into account both retailer and consumer preservation. As long as the retailer’s inventory is well preserved, its price will be low inducing consumers to stockpile and waste more food. Consumers may also waste more if their own preservation level is relatively high. The second essay focuses on governmental policies aimed at reducing consumer waste, such as a tax and a subsidy. Using microeconomic analysis, closed-form solutions for a social-optimal food waste tax and subsidy are derived. The government may impose this tax to increase the cost of waste disposal for households while using tax revenue to sponsor food preservation efforts. It is shown that the tax might not be an effective instrument if the responsiveness of food waste to this tax is low. Finally, the third essay investigates the impact of a nutrition education program on school-cafeteria waste. This program was implemented to promote the health benefits of consuming fruits and vegetables among elementary school children. Comparing food waste data in the treatment and control groups, we found no statistically significant evidence of either increased selection or consumption of fruits and vegetables in the treatment group.

Due to restricted budgets of relief organizations, costs of hiring transportation service providers steer distribution decisions and limit the impact of disaster relief. To improve the success of future humanitarian operations, it is of paramount importance to understand this relationship in detail and to identify mitigation actions, always considering the interdependencies between multiple independent actors in humanitarian logistics. In this paper, we develop a game-theoretic model in order to investigate the influence of transportation costs on distribution decisions in long-term relief operations and to evaluate measures for improving the fulfillment of beneficiary needs. The equilibrium of the model is a Generalized Nash Equilibrium, which has had few applications in the supply chain context to date. We formulate it, utilizing the construct of a Variational Equilibrium, as a Variational Inequality and perform numerical simulations in order to study the effects of three interventions: an increase in carrier competition, a reduction of transportation costs and an extension of framework agreements. The results yield important implications for policy makers and humanitarian organizations (HOs). Increasing the number of preselected carriers strengthens the bargaining power of HOs and improves impact up to a certain limit. The limit is reached when carriers set framework rates equal to transportation unit costs. Reductions of transportation costs have a consistently positive, but decreasing marginal benefit without any upper bound. They provide the highest benefit when the bargaining power of HOs is weak. On the contrary, extending framework agreements enables most improvements when the bargaining power of HOs is strong.

Cloud computing is a multi billion dollar industry, based around outsourcing the provisioning and maintenance of computing resources. In particular, Infrastructure as a Service (IaaS) enables customers to purchase virtual machines in order to run arbitrary software. IaaS customers are given the option to purchase priority access, while providers choose whether customers are preempted based on priority level. The customer decision is based on their tolerance for preemption. However, this decision is a reaction to the provider choice of preemption policy and cost to purchase priority. In this work, a non-cooperative game is developed for an IaaS system offering resource reservations. An unobservable $M|G|1$ queue with priorities is used to model customer arrivals and service. Customers receive a potential priority from the provider, and choose between purchasing a reservation for that priority and accepting the lowest priority for no additional cost. Customers select the option which minimizes their total cost of waiting. This decision is based purely on statistics, as customers cannot communicate with each other. This work presents the impact of the provider preemption policy choice on the cost customers will pay for a reserved instance. A provider may implement a policy in which no customers are preempted (NP); a policy in which all customers are subject to preemption (PR); or a policy in which only the customers not making reservations are subject to preemption (HPR). It is shown that only the service load impacts the equilibrium possibilities in the NP and PR policies, but that the service variance is also a factor under the HPR policy. These factors impact the equilibrium possibilities associated to a given reservation cost. This work shows that the cost leading to a given equilibrium is greater under the HPR policy than under the NP or PR policies, implying greater incentive to purchase reservations. From this it is proven that a provider maximizes their potential revenue from customer reservations under an HPR policy. It is shown that this holds in general and under the constraint that the reservation cost must correspond to a unique equilibrium. / 2020-06-03T00:00:00Z

Os leilões na Internet têm ganhado muita popularidade, tornando-se uma das mais bem sucedidas formas de comércio eletrônico na atualidade. Apresento um modelo teórico para descrever um leilão ascendente, semelhante ao que ocorre na eBay, e verifico suas previsões comportamentais através de dois experimentos. Os resultados mostraram um distanciamento grande entre as previsões teóricas e o que foi observado na prática, no que se refere às estratégias utilizadas, mas acredito que isso se deva à falta de experiência dos participantes dos experimentos. Desenvolvo, então, programas que automatizam a coleta de dados de leilões de selos na eBay e analiso as variáveis que influenciam preços, número de compradores e lances iniciais (preços mínimos). Não houve surpresas em tal análise, no sentido de observar-se resultados contra-intuitivos, mas destaco a reputação dos vendedores como fator relevante para a determinação de preços finais e número de compradores participantes. Além disso, também destaco a ocorrência da submissão tardia de lances, fenômeno recorrente nos leilões na Internet. Proponho, por fim, um método simples que busca determinar o tipo de modelo de leilão, se de valor comum ou de valor privado, e aplico o método nos dados obtidos dos leilões de selos. O resultado foi o de que os leilões analisados estão enquadrados no modelo de valor comum. / Online auctions are one of the most popular and successful types of electronic commerce nowadays. I present a theoretical framework to address the kind of ascending auction implemented at eBay, and I check its predictions through two experiments. The results of the experiments did not confirm the theory, but I believe this is due to the bidders’ lack of previous experience. I also present an algorithm that automatically gathers data from auctions of stamps at eBay. These data is then used on an exploratory analysis that tries to shed some light on the determinants of final prices, minimum bids and the number of bidders. There were no surprises in this analysis, but I would highlight the measurable effect that seller’s reputation has on final prices and the number of bidders. Furthermore, it was possible to observe the occurrence of late bidding. At last, I propose a simple method that determines to which paradigm the on-line auction of stamps at eBay belongs: private value or common value. The result was that the auction of stamps at eBay belongs to the common value paradigm.

Thesis advisor: Kenji Hayao / Thesis advisor: Hiroshi Nakazato / The most stunning example of two historical figures working both together and against one another to fashion a shared goal is the demonstration of power and compromise displayed by Count Camillo Benso di Cavour and Giuseppe Garibaldi during the Sicilian Revolution of 1860 and additional events during the greater Italian Risorgimento. This thesis is an attempt to uncover the bargaining strategies utilized by Cavour and Garibaldi throughout their political interactions as well as reach important conclusions concerning the use of interpersonal relationships to aid, not hinder, the outcome of a common political aim. This case study focuses on the years from 1852 to 1870, but specifically looks at 1859 to 1861, largely considering the theoretical framework of political game theory as outlined by Thomas Schelling. After forming two distinct hypotheses regarding both the competitive and cooperative nature of the two men's relationship, this thesis finds a greater cooperative characteristic to their historic interactions, although both hypotheses contribute to a relationship that formed the state of Italy. / Thesis (BA) — Boston College, 2008. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: International Studies. / Discipline: International Studies Honors Program.

Thesis advisor: Robert Murphy / Thesis advisor: Hiroshi Nakazato / The majority of scholarship surrounding the late 2000s financial crisis explores the enabling factors that contributed to the subprime bubble and caused it to burst. This study’s purpose is to evaluate systemic risk and the near collapse of the financial sector in 2008. Several factors, including derivatives innovation, the rise of a parallel banking industry, and the securitization boom, heightened systemic fragility. I add to financial contagion literature by constructing a stochastic game theory model of institutional decision-making under the auspices of a severe liquidity shortage. Moreover, I will employ this model to evaluate the government’s regulatory program during the crisis. I find that the government’s ad hoc interventions and non-interventions significantly contributed to the atmosphere of uncertainty and exacerbated the crisis’ ill effects. I go on to evaluate the Dodd-Frank Act in light of those conclusions and suggest an alternate method of financial reform. / Thesis (BA) — Boston College, 2011. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: International Studies Honors Program. / Discipline: International Studies.