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We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…

We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…

Recently, Artificial Intelligence (AI) technology use has been rising in sports to reach decisions of various complexity. At a relatively low complexity level, for example, major tennis tournaments replaced human line judges with Hawk-Eye…

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…

We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…

The presence or absence of winner-loser effects is a widely discussed phenomenon across both sports and psychology research. Investigation of such effects is often hampered by the limited availability of data. Online chess has exploded in…

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…

In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…

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…

In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the online rating algorithms which estimate the skills after each new…

Assessing the skill level of players to predict the outcome and to rank the players in a longer series of games is of critical importance for tournament play. Besides weaknesses, like an observed continuous inflation, through a steadily…

The Elo rating system is widely adopted to evaluate the skills of (chess) game and sports players. Recently it has been also integrated into machine learning algorithms in evaluating the performance of computerised AI agents. However, an…

While conventional ranking systems focus solely on maximizing the utility of the ranked items to users, fairness-aware ranking systems additionally try to balance the exposure for different protected attributes such as gender or race. To…

Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth.…

We present a physics-inspired method for inferring dynamic rankings in directed temporal networks - networks in which each directed and timestamped edge reflects the outcome and timing of a pairwise interaction. The inferred ranking of each…

Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a…

AI-controlled characters in fighting games are expected to possess reasonably high skills and behave in a believable, human-like manner, exhibiting a diversity of play styles and strategies. Thus, the development of fighting game AI…

Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…

Rating systems play a crucial role in evaluating player skill across competitive environments. The Elo rating system, originally designed for deterministic and information-complete games such as chess, has been widely adopted and modified…

Teammate performance evaluation fundamentally shapes intervention design in video games. However, our current understanding stems primarily from competitive E-Sports contexts where individual performance directly impacts outcomes. This…