The aim of this thesis is to verify the hypothesis on real data based on economic theory and these theories to confirm or reject. The first part deals with testing of hypotheses based on the game theory and tests whether tennis players play according to the minimax theory. The Hypotheses analyse the data for strong and weak players, considering their service, and verify which group of players converge in their strategies toward minimax theory assumptions. Specifically, theory components of the hypotheses are tested within this part: i) the probability of winning the game serving from the right side of a court is the same as the probability of winning the game serving from the left side, ii) this hypothesis will hold true rather in case of stronger players serving against weaker players than in case equally strong players playing against each other and iii) Based on the assumption that women do not excel distinctively in serving, the results in the women's matches will be worse in the minimax theory than results from men's matches. Hypotheses derived from the theory of elimination tournaments are tested in the second part of the diploma thesis. The hypotheses are analysed on the tennis data whether players make less effort in uneven tournaments, regardless of their position as favourite or outsider, than the theory presumes. The analysis of the above mentioned hypotheses was performed on the data from the Grand Slam tournaments in the years 2011 and 2012. Hypotheses are tested using both male and female data. The results obtained from analysis of the data confirm the hypotheses.

In der Arbeit wird das Konzept des fallbasierten Schließens zur Verwendung während der Minimax-Baumsuche in Spielbäumen vorgeschlagen. Die Auswirkungen von Änderungen an verschiedenen Parametern des Algorithmus werden anhand dazu durchgeführter Experimente dargestellt. Hervorzuheben sind besonders mehrere Auswahlstrategien, die den Lernprozess erheblich beschleunigen können.

The present paper is devoted to the investigation of the guided wave problem. This problem is formulated as the eigenvalue problem with a compact self-adjoint operator pencil. Applying the minimax principle for the compact operators in the Hilbert space we obtain a necessary and sufficient condition for the existence of a preassigned number of linearly independent guided modes. As a consequence of this result we also derive simple sufficient conditions, which can be easily applied in practice. We give a statement of the problem in a bounded domain and propose an efficient method for solving the problem.

Minimax D-optimal designs for regression models with heteroscedastic errors are studied and constructed. These designs are robust against possible misspecification of the error variance in the model. We propose a flexible assumption for the error variance and use a minimax approach to define robust designs. As usual it is hard to find robust designs analytically, since the associated design problem is not a convex optimization problem. However, the minimax D-optimal design problem has an objective function as a difference of two convex functions. An effective algorithm is developed to compute minimax D-optimal designs under the least squares estimator and generalized least squares estimator. The algorithm can be applied to construct minimax D-optimal designs for any linear or nonlinear regression model with heteroscedastic errors. In addition, several theoretical results are obtained for the minimax D-optimal designs. / Graduate

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This dissertation consists of three chapters that generally focus on the design of welfare-maximizing treatment assignment rules in heterogeneous populations with interactions. In the first two chapters, I focus on an important pre-step in the design of treatment assignment rules: inference for heterogeneous treatment effects in populations with interactions. In the final chapter, I and my co-authors study treatment assignment rules in the presence of social interaction in heterogeneous populations. In chapter one, I argue that statistical inference of heterogeneous treatment effects (HTEs) across predefined subgroups is complicated when economic units interact because treatment effects may vary by pretreatment variables, post-treatment exposure variables (that measure the exposure to other units’ treatment statuses), or both. It invalidates the standard hypothesis testing technique used to infer HTEs. To address the problem, I develop statistical methods (asymptotic and bootstrap) to infer HTEs and disentangle the drivers of treatment effects heterogeneity in populations where units interact. Specifically, I incorporate clustered interference into the potential outcomes model and propose kernel-based test statistics for the null hypotheses of (a) no HTEs by treatment assignment (or post-treatment exposure variables) for all pretreatment variables values; and (b) no HTEs by pretreatment variables for all treatment assignment vectors. To disentangle the source of heterogeneity in treatment effects, I recommend a multiple-testing algorithm. In addition, I prove the asymptotic properties of the proposed test statistics via a modern poissonization technique. As a robust alternative to the inferential methods I propose in chapter one, in chapter two, I design randomization tests of heterogeneous treatment effects (HTEs) when units interact on a single network. My modeling strategy allows network interference into the potential outcomes framework using the concept of network exposure mapping. I consider three null hypotheses that represent different notions of homogeneous treatment effects, but due to nuisance parameters and the multiplicity of potential outcomes, the hypotheses are not sharp. To address the issue of multiple potential outcomes, I propose a conditional randomization inference method that expands on existing methods. Additionally, I consider two techniques that overcome the nuisance parameter issue. I show that my conditional randomization inference method, combined with either of the proposed techniques for handling nuisance parameters, produces asymptotically valid p-values. Chapter three is based on a joint paper with Young Ki Shin and Seungjin Han. We study treatment assignment rules in the presence of social interaction in heterogeneous populations. We construct an analytical framework under the anonymous interaction assumption, where the decision problem becomes choosing a treatment fraction. We propose a multinomial empirical success (MES) rule that includes the empirical success rule of Manski (2004) as a special case. We investigate the non-asymptotic bounds of the expected utility based on the MES rule. / Dissertation / Doctor of Philosophy (PhD)

As of Russia's invasion of Ukraine we are now living in a time of full-scale war in Europe. This has ended a long period of relative peace and radically changed the security situation around the world. At the same time, the Swedish payment market has undergone a major shift in regards to cash versus digital payment. Today in Sweden, digital payments account for 96 percent of all payments, and these are made through private market actors. In response to the digitalization of the payment market, cash has been largely marginalized. Due to this coexistence, with a changed payment market and current security situation, this study aims to examine the risk management associated with payments during a potential invasion of Sweden, and the role of cash as a method of payment in wartime.  A fundamental principle assumed in this study is that the risks associated with payments in wartime are of the type Low Probability/High Consequence (LP/HC). These types of risks are particularly difficult to manage and there is thus reason to consider that the risk management of payments during an invasion may be insufficient. In this study we have constructed our own model, in order to analyze this issue, which includes three factors. These are lack of rationality, the public goods problem and hyperbolic discounting. The model aims to explain different problems and behaviors of decision-makers which may lead to inadequate risk management of LP/HC risks and thus deficient overall risk management of payments during an invasion. Throughout the study, we use the minimax-principle from game theory to further study the risk management of payments during an invasion as an LP/HC risk. In this qualitative study, eleven experts have been interviewed using a fictitious scenario of an invasion of Sweden. This functioned as the framework within which the experts then applied their insight to payments in war.  The results of the study show that the risk management of payments during an invasion has been overlooked and that lack of rationality, the public goods problem and hyperbolic discounting are all contributing factors to the problems we have identified. Further, the study defines that the payment system's lack of division of responsibilities and coordination, the unclear role of cash, as well as the cost issue and political game, are the determining factors regarding the lack of risk management around payments during an invasion. In conclusion, it is shown herein that cash does have a role to play during an invasion, but that extensive reformations must be made to increase the infrastructure around cash management.

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Monte Carlo tree search (MCTS) och Minimax är två sökalgoritmer som används inom artificiell intelligens och två-spelar-spel. I denna studie implementeras Minimax och MCTS som två AI-agenter för brädspelet Fyra i rad. Studien innehåller olika experiment i form av spelturneringar för att jämföra algoritmernas prestation. Algoritmerna beror på olika parametrar; Minimax har ett sökdjup och MCTS har en betänketid. Dessa parametrar undersöktes och ändrades för de olika turneringarna. Spelbräde utökades succesivt för att jämföra algoritmerna under olika förhållanden. Resultatet av studien visar att MCTS presterar bättre och vinner flest matcher på stora spelbräden och Minimax presterar bäst och vinner flest matcher på små spelbräden. Denna studie är ett bidrag till att få ytterligare förståelse för hur algoritmerna presterar och möjlighet till att utveckla de till mer avancerade och optimala algoritmer.