Related papers: How to Make Knockout Tournaments More Popular?
We want to introduce another smoothing approach by treating each geometric element as a player in a game: a quest for the best element quality. In other words, each player has the goal of becoming as regular as possible. The set of…
A tournament is an orientation of a graph. Each edge represents a match, directed towards the winner. The score sequence lists the number of wins by each team. Landau (1953) characterized score sequences of the complete graph. Moon (1963)…
Strong foundations in basic AI techniques are key to understanding more advanced concepts. We believe that introducing AI techniques, such as search methods, early in higher education helps create a deeper understanding of the concepts seen…
We introduce CUT, the class of 2-player partition games. These are NIM type games, played on a finite number of heaps of beans. The rules are given by a set of positive integers, which specifies the number of allowed splits a player can…
From the viewpoint of networks, a ranking system for players or teams in sports is equivalent to a centrality measure for sports networks, whereby a directed link represents the result of a single game. Previously proposed network-based…
We analyze the dynamics of competitions with a large number of players. In our model, n players compete against each other and the winner is decided based on the standings: in each competition, the mth ranked player wins. We solve for the…
Fairness has several interpretations in sports, one of them being that the rules should guarantee incentive compatibility, namely, a team cannot be worse off due to better results in any feasible scenario. The current seeding regime of the…
We study the Maker-Breaker tournament game played on the edge set of a given graph $G$. Two players, Maker and Breaker claim unclaimed edges of $G$ in turns, and Maker wins if by the end of the game she claims all the edges of a pre-defined…
We consider a game with two players, consisting of a number of rounds, where the first player to win $n$ rounds becomes the overall winner. Who wins each individual round is governed by a certain urn having two types of balls (type 1 and…
The rock-paper-scissors game is a model example of the on-going cyclic turnover typical of many ecosystems, ranging from the terrestrial and aquatic to the microbial. Here we explore the evolution of a rock-paper-scissors system where three…
Generalized Geography is a combinatorial game played on a directed graph. Players take turns moving a token from vertex to vertex, deleting a vertex after moving the token away from it. A player unable to move loses. It is well known that…
Constructing a suitable schedule for sports competitions is a crucial issue in sports scheduling. The round-robin tournament is a competition adopted in many professional sports. For most round-robin tournaments, it is considered…
This paper explores multi-entry strategies for betting pools related to single-elimination tournaments. In such betting pools, participants select winners of games, and their respective score is a weighted sum of the number of correct…
Round robin tournaments are omnipresent in sport competitions and beyond. We propose two new integer programming formulations for scheduling a round robin tournament, one of which we call the matching formulation. We analytically compare…
The game of bridge consists of two stages: bidding and playing. While playing is proved to be relatively easy for computer programs, bidding is very challenging. During the bidding stage, each player knowing only his/her own cards needs to…
Tournament organisers supposedly design rules such that a team cannot be strictly better off by exerting a lower effort. However, the European qualification tournaments for recent FIFA soccer World Cups are known to violate this…
The voting process is formalized as a multistage voting model with successive alternative elimination. A finite number of agents vote for one of the alternatives each round subject to their preferences. If the number of votes given to the…
We introduce the model of line-up elections which captures parallel or sequential single-winner elections with a shared candidate pool. The goal of a line-up election is to find a high-quality assignment of a set of candidates to a set of…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
In many real world elections, agents are not required to rank all candidates. We study three of the most common methods used to modify voting rules to deal with such partial votes. These methods modify scoring rules (like the Borda count),…