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We consider the problem of ranking $n$ players from partial pairwise comparison data under the Bradley-Terry-Luce model. For the first time in the literature, the minimax rate of this ranking problem is derived with respect to the Kendall's…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…
Suppose some cleverness score parameter is sufficiently interesting to be defined and then measured, perhaps for different strata of specialists or for the broader population. Such phenomena could have Gaussian distributions, when it comes…
Professional team sports provide an excellent domain for studying the dynamics of social competitions. These games are constructed with simple, well-defined rules and payoffs that admit a high-dimensional set of possible actions and…
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…
In this paper the results of a simulation of a prisoner's dilemma robin-round tournament are presented. In the tournament each participating strategy plays an iterated prisoner's dilemma against each other strategy (round-robin) and as a…
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…
The article presents the use of Monte Carlo Tree Search algorithms for the card game Lord of the Rings. The main challenge was the complexity of the game mechanics, in which each round consists of 5 decision stages and 2 random stages. To…
The traveling tournament problem (TTP) is to minimize the total traveling distance of all teams in a double round-robin tournament. In this paper, we focus on TTP-2, in which each team plays at most two consecutive home games and at most…
The paper suggests a family of paired comparison-based scoring procedures for ranking the participants of a Swiss system chess team tournament. We present the challenges of ranking in Swiss system, the features of individual and team…
Single-elimination tournaments are the standard paradigm both for the main tennis professional associations. Schedules are generated by allocating first seeded and then unseeded players with seeds prevented from encountering each other…
A co-evolutionary algorithm (CA) based chess player is presented. Implementation details of the algorithms, namely coding, population, variation operators are described. The alpha-beta or mini-max like behaviour of the player is achieved…
The most important factors which contribute to the efficiency of game-theoretical algorithms are time and game complexity. In this study, we have offered an elegant method to deal with high complexity of game theoretic multi-objective…
In this work we present a detailed analysis using the Markov chain theory of some versions of the truel game in which three players try to eliminate each other in a series of one-to-one competitions, using the rules of the game. Besides…
Tennis, like other games and sports, is governed by rules, including the rules that determine the winner of points, games, sets, and matches. If the two players are equally skilled -- each has the same probability of winning a point when…
In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation…
A knockout tournament is one of the most simple and popular forms of competition. Here, we are given a binary tournament tree where all leaves are labeled with seed position names. The players participating in the tournament are assigned to…
Traditional esports scouting workflows rely heavily on manual video review and aggregate performance metrics, which often fail to capture the nuanced decision-making patterns necessary to determine if a prospect fits a specific tactical…
The article presents research on the use of Monte-Carlo Tree Search (MCTS) methods to create an artificial player for the popular card game "The Lord of the Rings". The game is characterized by complicated rules, multi-stage round…
In competitive games, it is common to assign each player a real number rating signifying their skill level. A rating system is a procedure by which player ratings are adjusted upwards each time they win, or downwards each time they lose.…