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The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…
In J. Schwenk.(2018) ['What is the Correct Way to Seed a Knockout Tournament?' Retrieved from The American Mathematical Monthly], Schwenk identified a surprising weakness in the standard method of seeding a single elimination (or knockout)…
Tanking, the act of deliberately dropping points or losing a game in order to gain some other advantage, is usually seen as being against the spirit of sports. It can be even more serious if playing a draw is a (weakly) dominant strategy…
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…
Competitive tournaments appear in sports, politics, population ecology, and animal behavior. All of these fields have developed methods for rating competitors and ranking them accordingly. A tournament is intransitive if it is not…
This work presents and evaluates the ranking algorithm that has been used by Federation Internationale de Volleyball (FIVB) since 2020. The prominent feature of the FIVB ranking is the use of the probabilistic model, which explicitly…
An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…
The classical, complete-information two-player games assume that the problem data (in particular the payoff matrix) is known exactly by both players. In a now famous result, Nash has shown that any such game has an equilibrium in mixed…
We only consider finite structures. With every totally ordered set $V$ and a subset $P$ of $\binom{V}{2}$, we associate the underlying tournament ${\rm Inv}(\underline{V}, P)$ obtained from the transitive tournament $\underline{V}:=(V,…
A strong structural regularity of classes is found in soccer teams ranked by the Union of European Football Associations (UEFA) for the time interval 2009-2014. It concerns 424 to 453 teams according to the 5 competition seasons. The…
We describe a round robin scheduling problem for a competition played in two divisions, motivated by a scheduling problem brought to the second author by a local sports organisation. The first division has teams from 2n clubs, and is played…
In this work we study the ranking algorithm used by F\'ed\'eration Internationale de Football Association (FIFA); we analyze the parameters it currently uses, show the formal probabilistic model from which it can be derived, and optimize…
The non-scientific event of a soccer match is analysed on a strictly scientific level. The analysis is based on the recently introduced concept of a team fitness (Eur. Phys. J. B 67, 445, 2009) and requires the use of finite-size scaling. A…
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…
We initiate the study of incentive-compatible forecasting competitions in which multiple forecasters make predictions about one or more events and compete for a single prize. We have two objectives: (1) to incentivize forecasters to report…
Real-world problems typically require the simultaneous optimization of several, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables…
We present a new model of incomplete information games without private information in which the players use a distributionally robust optimization approach to cope with the payoff uncertainty. With some specific restrictions, we show that…
We present ten different strength-based statistical models that we use to model soccer match outcomes with the aim of producing a new ranking. The models are of four main types: Thurstone-Mosteller, Bradley-Terry, Independent Poisson and…
In this paper we bring a novel approach to the theory of tournament rankings. We combine two different theories that are widely used to establish rankings of populations after a given tournament. First, we use the statistical approach of…
A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem…