Knockout-Tournament Procedures for Large-Scale Ranking and Selection in Parallel Computing Environments

On one hand, large-scale ranking and selection (R&S) problems require a large amount of computation. On the other hand, parallel computing environments that provide a large capacity for computation are becoming prevalent today, and they are accessible by ordinary users. Therefore, solving large-scale R&S problems in parallel computing environments has emerged as an important research topic in recent years. However, directly implementing traditional stagewise procedures and fully sequential procedures in parallel computing environments may encounter problems because either the procedures require too many simulation observations or the procedures’ selection structures induce too many comparisons and too frequent communications among the processors. In this paper, inspired by the knockout-tournament arrangement of tennis Grand Slam tournaments, we develop new R&S procedures to solve large-scale problems in parallel computing environments. We show that no matter whether the variances of the alternatives are known or not, our procedures can theoretically achieve the lowest growth rate on the expected total sample size with respect to the number of alternatives and thus, are optimal in rate. Moreover, common random numbers can be easily adopted in our procedures to further reduce the total sample size. Meanwhile, the comparison time in our procedures is negligible compared with the simulation time, and our procedures barely request for communications among the processors.

WINNER PLAYS STRUCTURE IN RANDOM KNOCKOUT TOURNAMENTS

Suppose there arenplayers, with playerihaving valuevi> 0, and suppose that a game betweeniandjis won byiwith probabilityvi/(vi+vj). In the winner plays random knockout tournament, we suppose that the players are lined up in a random order; the first two play, and in each subsequent game the winner of the last game plays the next in line. Whoever wins the game involving the last player in line, is the tournament winner. We give bounds on players’ tournament win probabilities and make some conjectures. We also discuss how simulation can be efficiently employed to estimate the win probabilities.

Generalized Knockout Tournament Seedings

Generalized knockout tournament seedings for an arbitrary number of participants in one match are designed. Several properties of knockout tournament seedings are investigated. Enumeration results for knockout tournament seedings with different properties are obtained. Several new generalized knockout tournaments seedings are proposed and justified by a set of properties.

DIFFERENCES IN PUTTER TRAJECTORY AND PSYCHOPHYSIOLOGICAL VARIABLES BETWEEN PROFESSIONAL AND AMATEUR GOLFERS UNDER STRESS CONDITION

This study compared the differences in the putter trajectory and psychophysiological variables of winners and losers in a competitive putting game that targeted professional and amateur golfers under stress. Eight professional golfers (handicap: [Formula: see text]) and eight amateur golfers (handicap: [Formula: see text]) participated. To maximize the tension of the competition, the putting game was held in a single-elimination one-on-one knockout tournament with a single 2.1[Formula: see text]m putting competition for each group. In the case of a hole-in or a failure by both golfers, the game resumed until the winner was determined. To compare the golfers during the game, the maximum speed, moving length, and amplitude of the putter head during the back-swing and the follow-through were set as the motion variables; and psychological variables (heart rate, heart rate variability (HRV), and Competitive State Anxiety Inventory-2 (CSAI-2)) were analyzed. The results showed significant differences between the putter trajectory variables (maximum velocity and amplitude of the putter head during follow-through) of the groups, but no differences in the psychophysiological variables. In comparing winners and losers within each group, however, the professional group showed a difference in only the psychophysiological variables (HRV and self-confidence of CSAI-2), whereas the amateur group showed a difference in only one putter trajectory variable (follow-through length). It was quantitatively confirmed that factors that determine the outcome of the game differed at a technical level.

When Rigging a Tournament, Let Greediness Blind You

A knockout tournament is a standard format of competition, ubiquitous in sports, elections and decision making. Such a competition consists of several rounds. In each round, all players that have not yet been eliminated are paired up into matches. Losers are eliminated, and winners are raised to the next round, until only one winner exists. Given that we can correctly predict the outcome of each potential match (modelled by a tournament D), a seeding of the tournament deterministically determines its winner. Having a favorite player v in mind, the Tournament Fixing Problem (TFP) asks whether there exists a seeding that makes v the winner. Aziz et al. [AAAI’14] showed that TFP is NP-hard. They initiated the study of the parameterized complexity of TFP with respect to the feedback arc set number k of D, and gave an XP-algorithm (which is highly inefficient). Recently, Ramanujan and Szeider [AAAI’17] showed that TFP admits an FPT algorithm, running in time 2^{ O(k^2 log k)} n ^{O(1)}. At the heart of this algorithm is a translation of TFP into an algebraic system of equations, solved in a black box fashion (by an ILP solver). We present a fresh, purely combinatorial greedy solution. We rely on new insights into TFP itself, which also results in the better running time bound of 2^{ O(k log k)} n^{ O(1)} . While our analysis is intricate, the algorithm itself is surprisingly simple.

Game Outcome Uncertainty and Television Audience Demand: New Evidence from German Football

Despite its prominence in the economic literature, our knowledge regarding the role of game outcome uncertainty (GOU) in spectator decision-making is fairly limited. Even worse, studies testing the uncertainty of outcome hypothesis (UOH) by exploring TV demand for European football have further intensified the original ambiguity. In this paper, we revisit the role of GOU in spectator decision-making by testing the UOH with regard to two different sporting products: (1) domestic league and (2) knockout tournament games. Analyzing TV demand for almost 1,500 German football games, we find support for the UOH in league, though not in knockout tournament games.