Related papers: How to Make Knockout Tournaments More Popular?
Consider a very simple class of (finite) games: after an initial move by nature, each player makes one move. Moreover, the players have common interests: at each node, all the players get the same payoff. We show that the problem of…
Cricket is unarguably one of the most popular sports in the world. Predicting the outcome of a cricket match has become a fundamental problem as we are advancing in the field of machine learning. Multiple researchers have tried to predict…
We consider a biased version of Maker-Breaker domination games, which were recently introduced by Gledel, Ir{\v{s}}i{\v{c}}, and Klav{\v{z}}ar. Two players, Dominator and Staller, alternatingly claim vertices of a graph $G$ where Dominator…
Ranking is used in sport leagues to determine a champion and/or to decide on promotion/relegation of teams. Arguably, the best known ranking method relies on scores obtained by cumulating the points associated with the wins and the draws of…
We introduce and analyze the ordered Zeckendorf game, a novel combinatorial two-player game inspired by Zeckendorf's Theorem, which guarantees a unique decomposition of every positive integer as a sum of non-consecutive Fibonacci numbers.…
We consider a two-player search game on a tree $T$. One vertex (unknown to the players) is randomly selected as the target. The players alternately guess vertices. If a guess $v$ is not the target, then both players are informed in which…
Poker is a family of card games that includes many variations. We hypothesize that most poker games can be solved as a pattern matching problem, and propose creating a strong poker playing system based on a unified poker representation. Our…
Chess championships are often organised as a Swiss-system tournament, causing great challenges in ranking the participants due to the different strength of schedules and possible circular triads. The paper suggests that pairwise comparison…
A $k$-majority tournament $T$ on a finite set of vertices $V$ is defined by a set of $2k-1$ linear orders on $V$, with an edge $u \to v$ in $T$ if $u>v$ in a majority of the linear orders. We think of the linear orders as voter preferences…
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…
Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strategy for the opponent in the dual. For example, the Rothberger…
We give a new proof of the sufficiency of Landau's conditions for a non-decreasing sequence of integers to be the score sequence of a tournament. The proof involves jumping down a total order on sequences satisfying Landau's conditions and…
Counter reachability games are played by two players on a graph with labelled edges. Each move consists in picking an edge from the current location and adding its label to a counter vector. The objective is to reach a given counter value…
Penalty shootouts play a crucial role in the knockout stage of major football tournaments. Their importance has substantially increased from the 2021/22 season, when the Union of European Football Associations (UEFA) scrapped the away goals…
We study two-player games with alternating moves played on infinite trees. Our main focus is on the case where the trees are full (regular) and the winning set is open (with respect to the product topology on the tree). Gale and Stewart…
We study the dominating set problem in an online setting. An algorithm is required to guarantee competitiveness against an adversary that reveals the input graph one node at a time. When a node is revealed, the algorithm learns about the…
Models in which the number of goals scored by a team in a soccer match follow a Poisson distribution, or a closely related one, have been widely discussed. We here consider a soccer match as an experiment to assess which of two teams is…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
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…
Scoring rules aggregate individual rankings by assigning some points to each position in each ranking such that the total sum of points provides the overall ranking of the alternatives. They are widely used in sports competitions consisting…