A balanced tournament design of order <I>n</I>, BTD(<I>n</I>), defined on a 2<I>n</I>-set<I> V</i>, is an arrangement of the all of the (2<I>n</i>2) distinct unordered pairs of elements of <I>V</I> into an <I>n</I> X (2<I>n</i> - 1) array such that (1) every element of <I>V</i> occurs exactly once in each column and (2) every element of <I>V</I> occurs at most twice in each row. We will show that there exists a BTD(<i>n</i>) for <i>n</i> a positive integer, <i>n</i> not equal to 2. For <I>n</i> = 2, a BTD (<i>n</i>) does not exist. If the BTD(<i>n</i>) has the additional property that it is possible to permute the columns of the array such that for every row, all the elements of<I> V</I> appear exactly once in the first <i>n</i> pairs of that row and exactly once in the last <i>n</i> pairs of that row then we call the design a partitioned balanced tournament design, PBTD(<I>n</I>). We will show that there exists a PBTD (<I>n</I>) for <I>n</I> a positive integer, <I>n</I> is greater than and equal to 5, except possibly for <I>n</I> an element of the set {9,11,15}. For <I>n</I> less than and equal to 4 a PBTD(<I>n</I>) does not exist.

A balanced tournament design of order <I>n</I>, BTD(<I>n</I>), defined on a 2<I>n</I>-set<I> V</i>, is an arrangement of the all of the (2<I>n</i>2) distinct unordered pairs of elements of <I>V</I> into an <I>n</I> X (2<I>n</i> - 1) array such that (1) every element of <I>V</i> occurs exactly once in each column and (2) every element of <I>V</I> occurs at most twice in each row. We will show that there exists a BTD(<i>n</i>) for <i>n</i> a positive integer, <i>n</i> not equal to 2. For <I>n</i> = 2, a BTD (<i>n</i>) does not exist. If the BTD(<i>n</i>) has the additional property that it is possible to permute the columns of the array such that for every row, all the elements of<I> V</I> appear exactly once in the first <i>n</i> pairs of that row and exactly once in the last <i>n</i> pairs of that row then we call the design a partitioned balanced tournament design, PBTD(<I>n</I>). We will show that there exists a PBTD (<I>n</I>) for <I>n</I> a positive integer, <I>n</I> is greater than and equal to 5, except possibly for <I>n</I> an element of the set {9,11,15}. For <I>n</I> less than and equal to 4 a PBTD(<I>n</I>) does not exist.

In this dissertation, I examine changes in risk-taking behavior, beliefs, and self-deception induced by changes in policy and behavior. Specifically, Chapter II examines player performance and risk-taking behavior in tournament environments which include eliminations in the middle of the tournament. I find that when players face elimination, they perform better and take risks more often. In addition, when facing elimination, players are more likely to have those risks pay off. Turning to the interaction between public policy and personal beliefs, Chapter III explores how public policy affects beliefs in the context of same-sex marriage. Exploiting the timing of the legalization of same-sex marriage, I find that legalization induces an increase in the proportion of people who have strong beliefs on same-sex marriage. I also find a substantial increase in measured state-level polarization due to legalization. Finally, Chapter IV presents the results of an experiment designed to uncover how self-confidence and self-deception change after performing dishonest behavior. In an online experimental laboratory, participants who cheated have higher confidence in their ability even when the opportunity to cheat is not present. In addition, participants who cheated, and were rewarded for cheating with a high reward, had higher beliefs in their ability. This dissertation includes unpublished co-authored material.

Thesis(M.S.)--Auburn University, 2006. / Abstract. Includes bibliographic references.

Seymour’s distance two conjecture states that in any digraph there exists a vertex (a “Seymour vertex”) that has at least as many neighbors at distance two as it does at distance one. We explore the validity of probabilistic statements along lines suggested by Seymour’s conjecture, proving that almost surely there are a “large” number of Seymour vertices in random tournaments and “even more” in general random digraphs.

The results of a round robin tournament can be represented as a matrix of zeros and ones, by ordering the players and placing a one in the (i,j) position if player i beat player j, and zeros otherwise. These matrices, called tournament matrices, can be represented by graphs, called tournament graphs. They have been the subject of much research and study, yet there have been few attempts to give a wide exposition on the subject. Those that have been done tend to focus on the graph theoretical aspects of tournaments. S. Ree and Y. Koh did write a brief survey from the matrix viewpoint in 1998, but it was not complete and not published. This paper is an attempt to give an exposition on tournament matrices. Recent research will be presented, some new ideas and properties will be proposed, and a few applications of the material will be reviewed.

In this thesis we consider a few results related to the Zermelo and Extended Zermelo Model as well as outline some partial results and open problems related thereto. First we will analyze a discrete dynamical system considering under what conditions the convergence of this dynamical system predicts the outcome of the Extended Zermelo Model. In the following chapter we will focus on the Zermelo Model by giving a method for simplifying the derivation of Zermelo ratings for tournaments in terms of specific types of strongly connected components. Following this, the idea of stability of a tournament will be discussed and an upper bound will be obtained on the stability of three-team tournaments. Finally, we will conclude with some partial results related to the topics presented in the previous chapters.

<p>Turniri su najvi&scaron;e istraživana klasa orijentisanih grafova. U tezi su prezentovana dva tipa rezultata. Prvi se odnosi na tzv. neizbežne podgrafove. Obuhvata Hamiltonove bajpase, podgrafove C(<em>n, i</em>) i alternativne Hamiltonove konture. Drugi se bavi problemima frekvencija skorova u običnim, bipartitnim i 3-partitnim turnirima.</p> / <p>Tournaments are the most investigated class of oriented graphs. Two type of results are presented in the thesis. First one is related to so called unavoidable subgraphs. It discusses Hamiltonian bypasses, subgraphs C(n, i) and antidirected Hamiltonian cycles. The second deals with problems of score frequencies in ordinary, bipartite and 3-partite tournaments.</p>

Essay 1: The Determinants of the Convexity in the Flow-Performance Relationship There is substantial evidence that the flow-performance relationship of mutual funds is convex. In this work, I empirically investigate the determinants of such convexity. In particular, I study the impact that fund fees (marketing and non-marketing fees) and the uncertainty related to the replacement option of fund production factors (managerial ability and investment strategy) have on the convexity of the flow-performance relationship. I also analyze the impact of the priors about managerial ability and idiosyncratic risk on such convexity. The evidence suggests that marketing fees are positively related to the convexity of the flow-performance relationship. In addition, non-marketing fees do not have a negative impact on this convexity. The evidence associated with the value of the managerial and investment replacement option is mixed. Consistent with investment restrictions being relevant in explaining investors’ allocation decisions, sector, index, and hedge funds exhibit lower convexity in their flow-performance relationship than respectively diversified, non-index, and mutual funds. Finally, the dispersion of the priors about managerial ability and idiosyncratic risk are positively related to the convexity in the flow-performance relationship. Essay 2: Implicit Incentives and Tournament Behavior in the Mutual Fund Industry The convexity of the flow-performance relationship in the mutual fund industry produces implicit incentives for mutual fund managers to modify risk-taking behavior as a function of their prior performance (Brown, Harlow, and Starks (1996)). Rather than focusing only on tournament behavior, I investigate the link between the determinants of the convexity in the flow-performance relationship and the inter-temporal risk-shifting behavior of a fund’s manager. Hence, I examine how the sources of implicit compensation incentives shape tournament behavior. The evidence indicates that the relationship between changes in managers’ relative risk choices and mid-year performance is non-monotonic (U-shaped). Higher convexity in the flow-performance relationship increases the convexity of the U-shaped tournament behavior. For extreme performers, an increase in the convexity of the flow-performance relationship directly translates into higher risk-taking incentives. For average performers, the incentive to increase risk produced by the convexity in the compensation schedule is counterbalanced by an increase in the risk of termination. I find that the uncertainty about managerial ability, marketing efforts, and the size of family complexes affect the convexity of the U-shaped tournament behavior. These results are robust to the consideration of termination risks due to funds’ organizational form, investment objectives, or past performance. My results suggest that the risk strategies of younger funds, funds spending more on marketing, funds belonging to smaller families, sector funds, funds that are team-managed, or funds that have experienced consistent poor performance are more sensitive to intermediate performance.

Thesis(M.S.)--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references (p.57-62).