Essays on tournament design

The focus of the dissertation is on the informational utility of tournaments. We leave the incentive provision problem aside and essentially view tournaments as estimators of the unobserved ranking of players. We characterize such estimators quantitatively by their predictive power---a measure of how reliably a tournament identifies better players. This view of tournaments is also relatively new in the literature, although organizers' objectives stemming from it are important in many applications. In situations such as recruitment and promotion in firms or selection of public finance projects, a reasonable organizer's objective would be maximization of the predictive power. In sports, where uncertainty and upsets increase the "entertainment value" of tournaments for spectators, organizers may tend to minimize the predictive power. Throughout the dissertation we mainly address the decision problem of an organizer who seeks to maximize the predictive power of a tournament.; The dissertation consists of a literature review and three essays. The first essay is co-authored by Andreas Ortmann, while the second and the third essays are single-authored.; In the first essay, "Three prominent tournament formats: predictive power and costs", we explore the predictive power of three benchmark tournament formats---contests, binary elimination tournaments, and round-robin tournaments. For each of the three formats we develop combinatorial techniques that give analytical expressions for predictive power. One interesting finding is that predictive power may depend nonmonotonically on the number of competitors and the overall noise level. We also show which of the three formats is preferred by an organizer whose objective is to select the best player most accurately in the presence of costs.; In the second essay, "The predictive power of composite noisy tournaments," we propose a novel approach to construction of complex tournament formats out of elementary sub-tournaments ("building blocks"). The set of admissible building blocks is determined institutionally by players' specific activities. Once the building blocks are defined, the proposed algorithm constructs all possible tournament formats satisfying certain natural constraints. As an illustration, we consider composite tournament formats built out of generalized contests of n players with m winners and explore their predictive power. It is shown that the predictive power is maximized by multi-stage formats that slowly eliminate weaker players. Such formats are the most costly ones, and the organizer will switch to other formats as costs increase.; In the third essay, "Some additional properties of tournament formats," we discuss seeding in binary elimination tournaments, and marginal distributions of players' scores in round-robin tournaments. Seeding can be applied as an additional control mechanism by an organizer who has some a priori knowledge about players' ranking. We discuss how the predictive power of binary elimination tournaments is influenced by seeding in various regimes, and show that in some situations an optimal seeding scheme that maximizes the predictive power can be identified. Marginal distributions of scores in round-robin tournaments show what is the probability for a particular player to get a certain number of points. Our closed-form expression for this probability constitutes an interesting mathematical result. (Abstract shortened by UMI.)...