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The main challenge of combinatorial game theory is to handle combinatorial chaos, if one player knows the strategy better than his opponent, he is able to determine the exact results of a game. If both players are qualified competitor, the…
"The chance to win given a certain move" is an easily obtainable quantity from data and often quoted in gaming statistics. It is also the fundamental quantity that reinforcement learning AI bases on. Unfortunately, this conditional…
We construct a statistical ensemble of games, where in each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the…
Boosting algorithms enjoy strong theoretical guarantees: when weak learners maintain positive edge, AdaBoost achieves geometric decrease of exponential loss. We study how to incorporate group fairness constraints into boosting while…
Fairness in machine learning is crucial when individuals are subject to automated decisions made by models in high-stake domains. Organizations that employ these models may also need to satisfy regulations that promote responsible and…
Gameplay under various forms of uncertainty has been widely studied. Feldman et al. (2010) studied a particularly low-information setting in which one observes the opponent's actions but no payoffs, not even one's own, and introduced an…
With the increasing pervasive use of machine learning in social and economic settings, there has been an interest in the notion of machine bias in the AI community. Models trained on historic data reflect biases that exist in society and…
We present the first reinforcement-learning model to self-improve its reward-modulated training implemented through a continuously improving "intuition" neural network. An agent was trained how to play the arcade video game Pong with two…
We analyze a game introduced by Andy Niedermaier, where $p$ players take turns throwing a dart at a dartboard. A player is eliminated unless his dart lands closer to the center than all previously thrown darts, in which case he goes to the…
Fair machine learning is receiving an increasing attention in machine learning fields. Researchers in fair learning have developed correlation or association-based measures such as demographic disparity, mistreatment disparity, calibration,…
The authors propose a parametric model called the arena model for prediction in paired competitions, i.e. paired comparisons with eliminations and bifurcations. The arena model has a number of appealing advantages. First, it predicts the…
In some athletic races, such as cycling and types of speed skating races, athletes have to complete a relatively long distance at a high speed in the presence of direct opponents. To win such a race, athletes are motivated to hide behind…
Consider a game where Alice generates an integer and Bob wins if he can factor that integer. Traditional game theory tells us that Bob will always win this game even though in practice Alice will win given our usual assumptions about the…
A checkers-like model game with a simplified set of rules is studied through extensive simulations of agents with different expertise and strategies. The introduction of complementary strategies, in a quite general way, provides a tool to…
Paired comparison data considered in this paper originate from the comparison of a large number N of individuals in couples. The dataset is a collection of results of contests between two individuals when each of them has faced n opponents,…
This paper proposes an optimization algorithm based on how human fight and learn from each duelist. Since this algorithm is based on population, the proposed algorithm starts with an initial set of duelists. The duel is to determine the…
Patterns of wins and losses in pairwise contests, such as occur in sports and games, consumer research and paired comparison studies, and human and animal social hierarchies, are commonly analyzed using probabilistic models that allow one…
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…
A \emph{fair competition}, based on the concept of envy-freeness, is a non-eliminating competition where each contestant (team or individual player) may not play against all other contestants, but the total difficulty for each contestant is…
We conducted an experiment where participants played a perfect-information game against a computer, which was programmed to deviate often from its backward induction strategy right at the beginning of the game. Participants knew that in…