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Over the last decade, extensive research has been conducted on the algorithmic aspects of designing single-elimination (SE) tournaments. Addressing natural questions of algorithmic tractability, we identify key properties of input instances…
Challenge the champ tournaments are one of the simplest forms of competition, where a (initially selected) champ is repeatedly challenged by other players. If a player beats the champ, then that player is considered the new (current) champ.…
A tournament is a complete directed graph. It is well known that every tournament contains at least one vertex v such that every other vertex is reachable from v by a path of length at most 2. All such vertices v are called *kings* of 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…
Given a mapping from a set of players to the leaves of a complete binary tree (called a seeding), a knockout tournament is conducted as follows: every round, every two players with a common parent compete against each other, and the winner…
We introduce a new measure to capture fairness of a schedule in a single round robin (SRR) tournament when participants are ranked by strength. To prevent distortion of the outcome of an SRR tournament as well as to guarantee equal…
Bertrand et al. [1] (LMCS 2019) describe two-player zero-sum games in which one player tries to achieve a reachability objective in $n$ games (on the same finite arena) simultaneously by broadcasting actions, and where the opponent has full…
A central objective in Ramsey theory is determining whether restricted families of discrete structures necessarily contain substantially larger homogeneous substructures, compared to the unrestricted structures. In the setting of…
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…
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…
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,…
Tournament solutions provide methods for selecting the "best" alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out…
In knockout tournaments, players compete in successive rounds, with losers eliminated and winners advancing until a single champion remains. Given a tournament digraph $D$, which encodes the outcomes of all possible matches, and a…
A directed graph where there is exactly one edge between every pair of vertices is called a {\em tournament}. Finding the "best" set of vertices of a tournament is a well studied problem in social choice theory. A {\em tournament solution}…
An {\it inversion} of a tournament $T$ is obtained by reversing the direction of all edges with both endpoints in some set of vertices. Let ${\rm inv}_k(T)$ be the minimum length of a sequence of inversions using sets of size at most $k$…
In the tournament game two players, called Maker and Breaker, alternately take turns in claiming an unclaimed edge of the complete graph on n vertices and selecting one of the two possible orientations. Before the game starts, Breaker fixes…
A Condorcet voting scheme chooses a winning candidate as one who defeats all others in pairwise majority rule. We provide a review which includes the rigorous mathematical treatment for calculating the limiting probability of a Condorcet…
In sports competitions, teams can manipulate the result by, for instance, throwing games. We show that we can decide how to manipulate round robin and cup competitions, two of the most popular types of sporting competitions in polynomial…
The group draw of a sports tournament requires assigning teams to groups of (almost) the same size. The most important criteria for a draw procedure are balance, randomness, and transparency, which could not be satisfied simultaneously if…
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…