Optimal Strategies for Static Black-Peg AB Game With Two and Three Pegs

The AB~Game is a game similar to the popular game Mastermind. We study a version of this game called Static Black-Peg AB~Game. It is played by two players, the codemaker and the codebreaker. The codemaker creates a so-called secret by placing a color from a set of $c$ colors on each of $p \le c$ pegs, subject to the condition that every color is used at most once. The codebreaker tries to determine the secret by asking questions, where all questions are given at once and each question is a possible secret. As an answer the codemaker reveals the number of correctly placed colors for each of the questions. After that, the codebreaker only has one more try to determine the secret and thus to win the game. For given $p$ and $c$, our goal is to find the smallest number $k$ of questions the codebreaker needs to win, regardless of the secret, and the corresponding list of questions, called a $(k+1)$-strategy. We present a $\lceil 4c/3 \rceil-1)$-strategy for $p=2$ for all $c \ge 2$, and a $\lfloor (3c-1)/2 \rfloor$-strategy for $p=3$ for all $c \ge 4$ and show the optimality of both strategies, i.e., we prove that no $(k+1)$-strategy for a smaller $k$ exists

Positions- und Detektionsspiele

When it comes to the interaction of two ore more parties with individual aims, it’s all about finding an appropriate strategy. In most cases, the individual aim boils down to detection of information about the general situation or about your opponents and improvement of your own position. This goal becomes most clear and specific in the field of recreational games. In games like chess or tic-tac-toe, every player has complete information and the player’s position decides over win and loss. On the contrary, in games like poker every player tries to find out the value of the other players’ hands to play accordingly. This uncertainty of the opponent’s hand is the factor that makes the game interesting. Since all results of this thesis are connected to the field of game theory, it seems important to mention that this research field is not about having fun with different kinds of games, but, in the contrary, it’s about analysis of these games. The crucial difference between casual games and formal combinatorial games is that a combinatorial game is always assumed to be played by two players of infinite computational power. If the considered game is of complete information, the outcome of the game is already determined before it even started. The variety of games that are analyzed in this work ranges from popular recreational games as Mastermind over network-formation games to purely abstract games on graphs or hypergraph

Essays in Information Economics.

I study two economic responses to the challenges of copyright infringements and spam brought about by the birth of the Internet. These responses are anti-spam mechanisms and open contents. I derive conditions under which distribution and care level taken to avoid damages in open contents are socially efficient or inefficient. Then I report experimental results on the production of open contents. I compare free-riding, efficiency and spillover when there are large or small teams using non-modular or modular production. Lastly, I propose and evaluate an anti-spam mechanism called uncensored communication channel, which aims to entice spam-demanders and spam-suppliers to trade in there instead of the traditional email channels.Ph.D.InformationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75967/1/bchiao_1.pd

Complexity Theory for Discrete Black-Box Optimization Heuristics

A predominant topic in the theory of evolutionary algorithms and, more generally, theory of randomized black-box optimization techniques is running time analysis. Running time analysis aims at understanding the performance of a given heuristic on a given problem by bounding the number of function evaluations that are needed by the heuristic to identify a solution of a desired quality. As in general algorithms theory, this running time perspective is most useful when it is complemented by a meaningful complexity theory that studies the limits of algorithmic solutions. In the context of discrete black-box optimization, several black-box complexity models have been developed to analyze the best possible performance that a black-box optimization algorithm can achieve on a given problem. The models differ in the classes of algorithms to which these lower bounds apply. This way, black-box complexity contributes to a better understanding of how certain algorithmic choices (such as the amount of memory used by a heuristic, its selective pressure, or properties of the strategies that it uses to create new solution candidates) influences performance. In this chapter we review the different black-box complexity models that have been proposed in the literature, survey the bounds that have been obtained for these models, and discuss how the interplay of running time analysis and black-box complexity can inspire new algorithmic solutions to well-researched problems in evolutionary computation. We also discuss in this chapter several interesting open questions for future work.Comment: This survey article is to appear (in a slightly modified form) in the book "Theory of Randomized Search Heuristics in Discrete Search Spaces", which will be published by Springer in 2018. The book is edited by Benjamin Doerr and Frank Neumann. Missing numbers of pointers to other chapters of this book will be added as soon as possibl

The Role of Weaving in Smart material Systems

This thesis is an investigation into woven textile structures and weave construction methodologies. The main question at the heart of this research is what are smart textiles and what role/s can weaving play in the creation of such textiles in the future? A critical review of the literature led to a grammatical investigation and interpretation of the term smart textiles, and as a result a key differentiator between superficial and deep responsivity in constructed textiles is made: the latter is henceforth used to describe the uniqueness of smart textiles. The thesis proceeds to explore the fundamental engineering of textiles as material systems and by doing so, provide clues as to how fabrics could themselves be considered smart. Through this exploration, an original ‘textile anatomy’ mapping tool is presented with the aim to enhance and deepen current understanding of textiles and represent them as material systems instead. The hybrid research methodology that governed this investigation is unique. It relies on the creative tools of Design while also inherently applies the investigative methods of Science, Technology and Engineering. Weaving is explored through processes of making as an approach to develop smart textiles following an extensive historical review revealing that although methods of weave production have much evolved, the weave structures themselves have not changed at all for thousands of years. A series of experimental case studies are presented, which seek to explore and challenge current limitations of weaving for the creation of a new generation of material systems. As part of this work, the role of additive manufacturing was challenged, but its role as substitute manufacturing technique for textiles was accordingly rejected. This research finds that since weaving has become solely dependent on its machines, the structures produced through these processes of manufacturing are governed by such same specifications and limitations. As a result, in order to step away from current constraints, new assembly methodologies need to be revised. This is particularly applicable within the context of future (smart) material systems, and micro and nano fabrication techniques

The Role of Weaving in Smart Material Systems

This thesis is an investigation into woven textile structures and weave construction methodologies. The main question at the heart of this research is what are smart textiles and what role/s can weaving play in the creation of such textiles in the future? A critical review of the literature led to a grammatical investigation and interpretation of the term smart textiles, and as a result a key differentiator between superficial and deep responsivity in textiles is made: the latter is henceforth used to describe the uniqueness of smart textiles (chapter 3). The thesis proceeds to explore the fundamental engineering of textiles as material systems, and by doing so, provide clues as to how fabrics could themselves be considered smart. Through this exploration, an original ‘textile anatomy’ mapping tool is presented with the aim to enhance and deepen current understanding of textiles and represent them as material systems instead (chapters 4 and 5). The hybrid research methodology that governed this investigation is unique. It relies on the creative tools of Design while also inherently applies the investigative methods of Science, Technology and Engineering (chapter 2). Weaving is explored through processes of making as an approach to develop smart textiles following an extensive historical review revealing that although methods of weave production have much evolved, the weave structures themselves have not changed at all for thousands of years (chapter 5). A series of experimental case studies are presented, which therefore seek to explore and challenge current limitations of weaving for the creation of a new generation of material systems (chapter 6). As part of this practical work the alternative fabrication technology of additive manufacturing was considered, but its role as substitute manufacturing technique for textiles was accordingly rejected. This research finds that since weaving has become solely dependent on its machines, the structures produced through these processes of manufacturing are governed by such same specifications and limitations. As a result, in order to step away from current constraints, new assembly methodologies need to be revised. This is particularly applicable within the context of future (smart) material systems, and micro and nano fabrication techniques (chapters 7, 8 and 9)