Poker is a complex game to analyze. In this project we will use the mathematics of game theory to solve some simplified variations of the game. Probability is the building block behind game theory. We must understand a few concepts from probability such as distributions, expected value, variance, and enumeration methods to aid us in studying game theory. We will solve and analyze games through game theory by using different decision methods, decision trees, and the process of domination and simplification. Poker models, with and without cards, will be provided to illustrate optimal strategies. Extensions to those models will be presented, and we will show that optimal strategies still exist. Finally, we will close this paper with an original work to an extension that can be used as a medium to creating more extensions and, or, different games to explore.

The purpose of this paper is to investigate the effects of the Business Opportunity Projects (BOPs) that the Swedish Trade Council uses when promoting export for small enterprises. The Business Opportunity Projects have the same type of setup for all offices where the Swedish Trade Council is established and are subsidized by 60 percent from the government. A dataset on firms’ financial state on a ten year basis is used and survey interviews conducted in 2005/06 and 2007/08. From this data three types of methods are used; a calculations on expected values of return; a panel data model and a probit model.The results show that the expected return of one project is around 250 000 SEK and if the project is successful the average return is around 1 000 000 SEK. The governmental return is around 22 times the invested money. The probability of creating business volume directly or indirectly is around 45 percent. It is also shown that the projects have an impact on the export turnover of the participating firms. The effect comes after two years and it increases until four years after the BOP. The interpretation of the exact effect should be made with caution due to estimation issues. The result also indicates that the BOP generates around 1.5 employees on averages.The results show that the participating firms do not have advantage being larger, or being from the middle region of Sweden nor in a specific branch in order to have a successful project. Firms from north part of Sweden that have a slightly smaller chance of having a successful project, if the project is made in Western European offices, the firms have a higher probability to succeed compared to other offices.

This thesis studies the impact of sequential auction design on participant behavior from both a theoretical and an empirical viewpoint. In the first of the two analyses, three sequential auction designs are characterized and compared based on expected profitability to the participants. The optimal bid strategy is derived as well. One of the designs, the alternating design, is a new auction design and is a blend of the other two. It assumes that the ability to bid in or initiate an auction is given to each side of the market in an alternating fashion to simulate seasonal markets. The conditions for an equilibrium auction design are derived and characteristics of the equilibrium are outlined. The primary result is that the alternating auction is a viable compromise auction design when buyers and suppliers disagree on whether to hold a sequence of forward or reverse auctions. We also found the value of information on future private value for a strategic supplier in a two-period case of the alternating and reverse auction designs. The empirical work studies the cause of low aggregation of timber supply in reverse auctions of an online timber exchange. Unlike previous research results regarding timber auctions, which focus on offline public auctions held by the U.S. Forest Service, we study online private auctions between logging companies and mills. A limited survey of the online auction data revealed that the auctions were successful less than 50% of the time. Regression analysis is used to determine which internal and external factors to the auction affect the aggregation of timber in an effort to determine the reason that so few auctions succeeded. The analysis revealed that the number of bidders, the description of the good and the volume demanded had a significant influence on the amount of timber supplied through the online auction exchange. A plausible explanation for the low aggregation is that the exchange was better suited to check the availability for custom cuts of timber and to transact standard timber.

This thesis covers the uncertainty of empirical prediction. As opposed to objectivity, I will discuss the practicality of statistics. Practicality defined as "useful" in an unbiased sense, in relation to something in the external world that we care about. We want our model of prediction to give us unbiased inference whilst also being able to speak about something we care about. For the reasons explained, the inherent uncertainty of statistics undermines the unbiased inference for many methods. Bayesian Statistics, by valuing hypotheses is more plausible but ultimately cannot arrive at an unbiased inference. I posit the value theory of money as a concept that might be able to allow us to derive unbiased inferences from while still being something we care about. However, money is of instrumental value, ultimately being worth less than an object of “transcendental value.” Which I define as something that is worth more than money since money’s purpose is to help us achieve “transcendental value” under the value theory. Ultimately, as long as an individual has faith in a given hypothesis it will be worth more than any hypothesis valued with money. From there we undermine statistic’s practicality as it seems as though without the concept of money we have no manner of valuing hypotheses unbiasedly, and uncertainty undermines the “objective” inferences we might have been able to make.

The aim of this master thesis is primarily to develop a methodological framework for a contracting authority receiving an abnormally low bid. The theoretical part of the thesis outlines the basic terms and definitions, analyzes a public tender from the perspective of a contracting authority and defines an extremely low bid price. The practical part of the thesis applies the methodological framework for dealing with an extremely low bid price on the case study, where on the set of selected areas of mechanical items indicates possible views above the limit costs of individual items costing unit prices of construction work.

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„Nun sag, wie hast du’s mit der Messung im Labor?“ So oder ähnlich lautet die sich anhand dieser Arbeit ergebende Gretchenfrage bezüglich biomechanischer Auswertungen und Studien des Laufsports, welche unter Laborbedingungen durchgeführt werden. Hierbei wird angenommen, dass eine Messung im Labor eine valide experimentelle Operationalisierung des Ausdauerlaufens darstellt. Aufgrund der räumlichen Begrenzung kann lediglich eine vergleichsweise geringe Anzahl an einzelnen Versuchen aufgezeichnet werden. Für die statistische Auswertung werden dann zumeist einzelne Parameter der Zeitreihen berechnet, welche wiederum zusammengefasst durch Mittelwerte den Probanden repräsentieren müssen. Bei der Verwendung von diskreten Parametern reduziert sich die aufgenommene Information der Zeitreihe dabei erheblich. Damit einhergehend muss die Frage geklärt werden, ob die Variabilität eines Probanden anhand diskreter Werte oder anhand der gesamten Kurve Beachtung finden muss. Des Weiteren stellt sich die Frage inwieweit das arithmetische Mittel über eine große Anzahl an Versuchen als die den Probanden repräsentierende Kennzahl verwendet und dessen Variabilität mittels einer endlichen Anzahl an Wiederholungen charakterisiert werden kann. Für die Untersuchungen wurden zunächst zwei Studien durchgeführt, wobei die Aufzeichnung von Bodenreaktionskräften und der Winkelgeschwindigkeit bei 100 Läufen an je zwei Messtagen im Labor erfolgte. Die statistischen Auswertungen umfassen sowohl die Betrachtung der Konvergenz von Folgen kumulierter Mittelwerte, Standardabweichungen und Root Mean Square Errors für diskrete Parameter und die gesamten aufgezeichneten Signale der Bodenreaktionskräfte und Winkelgeschwindigkeit als auch die Untersuchung von Prädiktionsbändern. Zudem wurden unterschiedliche Algorithmen zur Bestimmung der minimalen Anzahl an aufzuzeichnenden Versuchen entwickelt. Diese beinhalten nichtlineare Regressionsmodelle für die Anpassung der kumulierten Fläche der Prädiktionsbänder gesamter Kurven und die Analyse der Differenzen aufeinanderfolgender Standardabweichungskurven. Zusammenfassend geht aus dieser Arbeit hervor, dass die postulierte ausreichende und stabile Charakterisierung eines Probanden anhand des arithmetischen Mittels sowie der vollständigen und soliden Beschreibung der Variabilität für diskrete Parameter nicht nachgewiesen werden konnte. Für gesamte Kurven ergab sich ein anderes Bild. Die Probanden konnten anhand der mittleren vertikalen Bodenreaktionskräfte sowie der Bodenreaktionskräfte in anterior-posterior Richtung stabil und ausreichend charakterisiert werden. Für die Bodenreaktionskräfte in mediolateraler Richtung und die Kurve der Winkelgeschwindigkeit wurde dies nicht bestätigt. Die Möglichkeit der Charakterisierung der Variabilität eines Probanden konnte zudem verifiziert werden. Durch Beibehaltung der ursprünglichen Messprozedur ist die Wahrscheinlichkeit sehr hoch, dass der begangene Fehler den Ausgang der statistischen Auswertung beeinflusst und damit Eigenschaften der vorliegenden Grundgesamtheit unter Umständen falsch widerspiegelt. Von einer Verwendung des Mittelwertes diskreter Parameter sollte daher abgesehen werden. Der Fehler sowie dessen unbekanntes Ausmaß sind zum Teil unkontrollierbar und dessen Auswirkungen auf weitere biomechanische Kenngrößen nicht überprüfbar. Die Annahme, dass eine Labormessung als valide experimentelle Operationalisierung des Ausdauerlaufens angesehen werden kann, ist damit hinfällig. Es ist zukünftig notwendig, die Erforschung neuer Aufnahme- und Auswerteprozeduren, die alternative Verwendung gesamter Kurven und die Entwicklung neuer Testverfahren zu forcieren.

In cryptography, periodic sequences with terms in F2 are used almost everywhere. These sequences should have large linear complexity to be cryptographically strong. In fact, the linear complexity of a sequence should be close to its period. In this thesis, we study the expected value for N-periodic sequences with terms in the finite field Fq. This study is entirely devoted to W. Meidl and Harald Niederreiter&rsquo / s paper which is &ldquo / On the Expected Value of the Linear Complexity and the k-Error Linear Complexity of Periodic Sequences&rdquo / We only expand this paper, there is no improvement. In this paper there are important theorems and results about the expected value of linear complexity of periodic sequences.

[pt] Neste trabalho apresentaremos a noção de valor esperado de uma variável aleatória, ou valor médio de uma quantidade aleatória, um conceito probabilístico extremamente importante e útil em diversas aplicações, mas que por razões históricas, não costuma ser ensinado no Ensino Médio. Além desse assunto, abordaremos também alguns problemas interessantes e desafiadores de Probabilidade, como por exemplo, questões dos vestibulares mais difíceis do País, como o do Instituto Militar de Engenharia (IME) e O Desafio em Matemática da PUC-Rio. Em várias das atividades propostas, ao longo nosso trabalho, iremos utilizar recursos computacionais como o Excel e o GeoGebra, e mostrar que podem ser fortes aliados ao ensino de Probabilidade e auxiliar no entendimento do conceito de Valor Esperado. / [en] In this dissertation we present the definition of the expected value of a random variable, an important probabilistic concept which is useful in many applications but which, for historical reasons, is not taught in high school in Brazil. We also discuss examples of interesting and challenging probability problems, including questions from some of the hardest exams in the country, such as the Vestibular for the Instituto Militar de Engenharia (IME) and the Desafio em Matemática of PUC-Rio. In many of the proposed activities, we use computational tools such as Excel and GeoGebra: these can become allies when teaching probability and help in the understanding of the concept of expected value.

This thesis presents various models to the fashion industry to predict the profits for some products. To determine the expected performance of each product in 2016, we used tools of game theory to help us identify the expected value. We went further and performed a simple linear regression and used scatter plots to help us predict further the performance of the products of Prada. We used tools of game theory, analytics, and statistics to help us predict the performance of some of Prada's products. We also used the Tableau platform to visualize an overview of the products' performances. All of these tools were used to aid in finding better predictions of Prada's product performances.