Related papers: Robust Value Maximization in Challenge the Champ T…
A tournament is a method to decide the winner in a competition, and describes the overall sequence in which matches between the players are held. While deciding a worthy winner is the primary goal of a tournament, a close second is to…
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.…
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…
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…
We consider a general class of round-robin tournament models of equally strong players. In these models, each of the $n$ players competes against every other player exactly once. For each match between two players, the outcome is a value…
We characterize robust tournament design -- the prize scheme that maximizes the lowest effort in a rank-order tournament where the distribution of noise is unknown, except for an upper bound, $\bar{H}$, on its Shannon entropy. The robust…
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 tournament graph is a complete directed graph, which can be used to model a round-robin tournament between $n$ players. In this paper, we address the problem of finding a champion of the tournament, also known as Copeland winner, which is…
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…
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…
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…
In the online learning with experts problem, an algorithm must make a prediction about an outcome on each of $T$ days (or times), given a set of $n$ experts who make predictions on each day (or time). The algorithm is given feedback on the…
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 consider two-player stochastic games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously;…
We consider the manipulability of tournament rules which map the results of $\binom{n}{2}$ pairwise matches and select a winner. Prior work designs simple tournament rules such that no pair of teams can manipulate the outcome of their match…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…
Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators' excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize…
We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…
The organizer of a machine learning competition faces the problem of maintaining an accurate leaderboard that faithfully represents the quality of the best submission of each competing team. What makes this estimation problem particularly…
We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…