Knockout tournaments constitute a popular format for organizing sports competitions. While prior results have shown that it is often possible to manipulate a knockout tournament by fixing the ...bracket, these results ignore the prevalent aspect of player seeds, which can significantly constrain the chosen bracket. We show that certain structural conditions that guarantee that a player can win a knockout tournament without seeds are no longer sufficient in light of seed constraints. On the other hand, we prove that when the pairwise match outcomes are generated randomly, all players are still likely to be knockout winners under the same probability threshold with seeds as without seeds. In addition, we investigate the complexity of deciding whether a manipulation is possible when seeds are present.
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 round of the knockout phase: teams from the same country cannot be drawn against each other. Its effects are explored in both theoretical and simulation models. An association constraint in the first round(s) is found to increase the likelihood of same nation matchups to approximately the same extent in each subsequent round. If the favourite teams are concentrated in some associations, they will have a higher probability to win the tournament under this policy but the increase is less than linear if it is used in more rounds. Our results might explain the recent introduction of the association constraint for both the knockout round play-offs with 16 teams and the Round of 16 in the UEFA Europa League and UEFA Europa Conference League.
The present book contains all the articles accepted and published in the Special Issue “Advances in Artificial Intelligence: Models, Optimization, and Machine Learning” of the MDPI Mathematics ...journal, which covers a wide range of topics connected to the theory and applications of artificial intelligence and its subfields. These topics include, among others, deep learning and classic machine learning algorithms, neural modelling, architectures and learning algorithms, biologically inspired optimization algorithms, algorithms for autonomous driving, probabilistic models and Bayesian reasoning, intelligent agents and multiagent systems. We hope that the scientific results presented in this book will serve as valuable sources of documentation and inspiration for anyone willing to pursue research in artificial intelligence, machine learning and their widespread applications.
We study competitions structured as hierarchically shaped single-elimination tournaments. We define optimal tournaments by maximizing attractiveness such that the topmost players will have the chance ...to meet in higher stages of the tournament. We propose a dynamic programming algorithm for computing optimal tournaments and we provide its sound complexity analysis. Based on the idea of the dynamic programming approach, we also develop more efficient deterministic and stochastic sub-optimal algorithms. We present experimental results obtained with the Python implementation of all the proposed algorithms regarding the optimality of solutions and the efficiency of the running time.
Suppose there are n players, with player i having value vi > 0, and suppose that a game between i and j is won by i with probability vi/(vi + vj). In the winner plays random knockout tournament, we ...suppose that the players are lined up in a random order; the first two play, and in each subsequent game the winner of the last game plays the next in line. Whoever wins the game involving the last player in line, is the tournament winner. We give bounds on players’ tournament win probabilities and make some conjectures. We also discuss how simulation can be efficiently employed to estimate the win probabilities.
This article focuses on the question of whether a certain candidate’s (player’s) chance to advance further in a tennis tournament can be increased when the ordering of the tournament can be ...controlled (manipulated by the organizers) according to his own preferences. Is it possible to increase the number of ranking points a player will receive? And most importantly, can it be done in reasonable computational time? The answers to these questions differ for different settings. e.g., the information available on the outcome of each game, the significance of the number of points gained or of the number of games won. We analyzed five different variations of these tournament questions. First the complexity hardness of trying to control the tournaments is shown. Then, the tools of parametrized complexity are used to investigate the source of the problems’ hardness. Specifically, we check whether this hardness holds when the size of the problem is bounded. The findings of this analysis show that it is possible under certain circumstances to control the tournament in favor of a specific candidate in order to help him advance further in the tournament.
A tournament graph over
n
players is weakly transitive at player
p
if it contains a Hamiltonian path
p
1
,
p
2
,
⋯
,
p
n
with
p
1
=
p
such that for all odd integers
i
≤
n
-
2
there is an arc from
...p
i
to
p
i
+
2
. We show that weak transitivity at
p
suffices to make player
p
win any extended stepladder tournament of degree at most two.
Fair Seeding in Knockout Tournaments Vu, Thuc; Shoham, Yoav
ACM transactions on intelligent systems and technology,
10/2011, Letnik:
3, Številka:
1
Journal Article
Recenzirano
We investigated the existence of fair seeding in knockout tournaments. We define two fairness criteria, both adapted from the literature: envy-freeness and order preservation. We show how to achieve ...the first criterion in tournaments whose structure is unconstrained, and prove an impossibility result for balanced tournaments. For the second criterion we have a similar result for unconstrained tournaments, but not for the balanced case. We provide instead a heuristic algorithm which we show through experiments to be efficient and effective. This suggests that the criterion is achievable also in balanced tournaments. However, we prove that it again becomes impossible to achieve when we add a weak condition guarding against the phenomenon of tournament dropout.
In this paper, neighborhood monotonicity is presented as a natural property for methods of ranking generalized tournaments (directed graphs with weighted edges). An extension of Zermelo’s classical ...method of ranking tournaments is shown to have this property. An estimate is made of the proportion of ordered pairs that all neighborhood-monotonic rankings of symmetric knockout tournaments have in common. Finally, numerical evidence for the asymptotic behavior of the extended Zermelo ranking of symmetric knockout tournaments is presented.
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