Related papers: How to Make Knockout Tournaments More Popular?
Knockout tournaments constitute a popular format for organizing sports competitions. While prior results have shown that it is often possible to manipulate a knockout tournament by fixing the bracket, these results ignore the prevalent…
A knockout tournament is one of the most simple and popular forms of competition. Here, we are given a binary tournament tree where all leaves are labeled with seed position names. The players participating in the tournament are assigned to…
In J. Schwenk.(2018) ['What is the Correct Way to Seed a Knockout Tournament?' Retrieved from The American Mathematical Monthly], Schwenk identified a surprising weakness in the standard method of seeding a single elimination (or knockout)…
Knockout tournaments, also known as single-elimination or cup tournaments, are a popular form of sports competitions. In the standard probabilistic setting, for each pairing of players, one of the players wins the game with a certain (a…
We propose a new tournament structure that combines the popular knockout tournaments and the round-robin tournaments. As opposed to the extremes of divisive elimination and no elimination, our tournament aims to eliminate the participants…
We consider a random knockout tournament among players $1, \ldots, n$, in which each match involves two players. The match format is specified by the number of matches played in each round, where the constitution of the matches in a round…
A set of $2^n$ candidates is presented to a commission. At every round, each member of this commission votes by pairwise comparison, and one-half of the candidates is deleted from the tournament, the remaining ones proceeding to the next…
This paper explores a novel way for analyzing the tournament structures to find a best suitable one for the tournament under consideration. It concerns about three aspects such as tournament conducting cost, competitiveness development and…
We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a…
We investigate a new tournament format that consists of a series of individual knockout tournaments; we call this new format a Serial Knockout Competition (SKC). This format has recently been adopted by the Professional Darts Corporation.…
Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the…
A tournament organizer must select one of $n$ possible teams as the winner of a competition after observing all $\binom{n}{2}$ matches between them. The organizer would like to find a tournament rule that simultaneously satisfies the…
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,…
A single-elimination (SE) tournament is a popular way to select a winner in both sports competitions and in elections. A natural and well-studied question is the tournament fixing problem (TFP): given the set of all pairwise match outcomes,…
Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning…
The classical paradox of social choice theory asserts that there is no fair way to deterministically select a winner in an election among more than two candidates; the only definite collective preferences are between individual pairs of…
League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest…
Tournaments are a widely used mechanism to rank alternatives in a noisy environment. This paper investigates a fundamental issue of economics in tournament design: what is the best usage of limited resources, that is, how should the…
The paper analyses how draw constraints influence the outcome of a knockout tournament. The research question is inspired by European club football competitions, where the organiser generally imposes an association constraint in the first…
We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…