Related papers: An Analysis of Tournament Structure
We consider a deterministic game with alternate moves and complete information, of which the issue is always the victory of one of the two opponents. We assume that this game is the realization of a random model enjoying some independence…
This research work aims to develop an analytical approach for optimizing team formation and predicting team performance in a competitive environment based on data on the competitors' skills prior to the team formation. There are several…
What are the chances of an ethical individual rising through the ranks of a political party or a corporation in the presence of unethical peers? To answer this question, I consider a four-player two-stage elimination tournament, in which…
In 2000 Allen Schwenk, using a well-known mathematical model of matchplay tournaments in which the probability of one player beating another in a single match is fixed for each pair of players, showed that the classical single-elimination,…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…
We study how individuals trade off outcome ("what") and process ("how") utility in high-stakes strategic decisions, namely professional tennis. Using optimality conditions and the second-service rule, we derive a sufficient condition for…
The score set of a tournament is defined as the set of its distinct out-degrees. In 1978, Reid proposed the conjecture that for any set of nonnegative integers $D$, there exists a tournament $T$ with a degree set $D$. In 1989, Yao presented…
The game of Knockout is a classic playground game played with two basketballs. This paper uses a Markov process to analyze each player's probability of winning the game given their starting position in line and shooting percentages,…
Winning competitive debates requires sophisticated reasoning and argument skills. There are unique challenges in the competitive debate: (1) The time constraints force debaters to make strategic choices about which points to pursue rather…
The score sequence of a tournament is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The problem of counting score sequences of a tournament with $n$ vertices is more than 100 years old (MacMahon 1920). In…
We study the density of fixed strongly connected subtournaments on 5 vertices in large tournaments. We determine the maximum density asymptotically for five tournaments as well as unique extremal sequences for each tournament. As a…
The Swiss-system is an increasingly popular competition format as it provides a favourable trade-off between the number of matches and ranking accuracy. However, there is no empirical study on the potential unfairness of Swiss-system chess…
Team assembly is a problem that demands trade-offs between multiple fairness criteria and computational optimization. We focus on four criteria: (i) fair distribution of workloads within the team, (ii) fair distribution of skills and…
The sequence counting the number of unique tournaments with n people is the same as the sequence counting non-tracking binary strings corresponding to n-2 radar observations with the tracking rule "3 out of 5 with loss 2." This fact allows…
The usual FIFA World Cup-TM group stage format is eight groups of four teams for a total of 32 teams. The top two teams from each group advance to the next round, resulting in a 16-team knockout stage. The next edition of the World Cup will…
The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. A directed graph is said to support M if its adjacency matrix is the pattern of M. If M is an orthogonal matrix, then a digraph which supports M…
In the game of cricket, the result of coin toss is assumed to be one of the determinants of match outcome. The decision to bat first after winning the toss is often taken to make the best use of superior pitch conditions and set a big…
A tournament is an orientation of a complete graph. We say that a vertex $x$ in a tournament $\vec T$ controls another vertex $y$ if there exists a directed path of length at most two from $x$ to $y$. A vertex is called a king if it…
I study optimal disclosure policies in sequential contests. A contest designer chooses at which periods to publicly disclose the efforts of previous contestants. I provide results for a wide range of possible objectives for the contest…