Related papers: Fixing Knockout Tournaments With Seeds
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 how robust the results of committee elections are to small changes in the input preference orders, depending on the voting rules used. We find that for typical rules the effect of making a single swap of adjacent candidates…
Reid conjectured that any finite set of non-negative integers is the score set of some tournament and Yao gave a non-constructive proof of Reid's conjecture using arithmetic arguments. No constructive proof has been found since. In this…
Every sport needs rules. Tournament design refers to the rules that determine how a tournament, a series of games between a number of competitors, is organized. This study aims to provide an overview of the tournament design literature from…
The determinant of a tournament $T$ is defined as the determinant of the skew-adjacency matrix of $T$. For a positive odd integer $k$, let $\mathcal{D}_k$ be the set of tournaments whose all subtournaments have determinant at most $k^2$.…
We consider the problem of inferring an unknown ranking of $n$ items from a random tournament on $n$ vertices whose edge directions are correlated with the ranking. We establish, in terms of the strength of these correlations, the…
We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an…
We consider the computational complexity of the question whether a certain strategy can be removed from a game by means of iterated elimination of dominated strategies. In particular, we study the influence of different definitions of…
Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…
Control and manipulation are two of the most studied types of attacks on elections. In this paper, we study the complexity of control attacks on elections in which there are manipulators. We study both the case where the "chair" who is…
Successive elimination of candidates is often a route to making manipulation intractable to compute. We prove that eliminating candidates does not necessarily increase the computational complexity of manipulation. However, for many voting…
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…
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),…
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…
We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
We consider two-player contests with the possibility of ties and study the effect of different tie-breaking rules on effort. For ratio-form and difference-form contests that admit pure-strategy Nash equilibrium, we find that the effort of…
A fundamental result in cake cutting states that for any number of players with arbitrary preferences over a cake, there exists a division of the cake such that every player receives a single contiguous piece and no player is left envious.…
Constructive election control considers the problem of an adversary who seeks to sway the outcome of an electoral process in order to ensure that their favored candidate wins. We consider the computational problem of constructive election…
We consider the recently introduced knotting-unknotting game, in which two players take turns resolving crossings in a knot diagram which initially is missing all its crossing information. Once the knot is fully resolved, the winner is…
Deep learning models benefit from rich (e.g., multi-modal) input features. However, multimodal models might be challenging to deploy, because some inputs may be missing at inference. Current popular solutions include marginalization,…