Related papers: Where to stand when playing darts?

In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large…

We consider a network of coupled agents playing the Prisoner's Dilemma game, in which players are allowed to pick a strategy in the interval [0,1], with 0 corresponding to defection, 1 to cooperation, and intermediate values representing…

Ensuring the security of networked systems is a significant problem, considering the susceptibility of modern infrastructures and technologies to adversarial interference. A central component of this problem is how defensive resources…

Recent results in the ML community have revealed that learning algorithms used to compute the optimal strategy for the leader to commit to in a Stackelberg game, are susceptible to manipulation by the follower. Such a learning algorithm…

We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing…

We study concentration properties of random vectors of the form $AX$, where $X = (X_1, ..., X_n)$ has independent coordinates and $A$ is a given matrix. We show that the distribution of $AX$ is well spread in space whenever the…

We study a setting in which two players play a (possibly approximate) Nash equilibrium of a bimatrix game, while a learner observes only their actions and has no knowledge of the equilibrium or the underlying game. A natural question is…

In this paper we examine the effectiveness of five mathematical models used to predict the outcomes of amateur darts games. These models not only predict the outcomes at the start of the game, but also update their estimations as the game…

This paper considers a class of two-player zero-sum games on directed graphs whose vertices are equipped with random payoffs of bounded support known by both players. Starting from a fixed vertex, players take turns to move a token along…

Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players' strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces…

In the game "Super Six", after successfully getting rid of a stick by rolling with the die a number that is not occupied, the player has the choice to continue to roll the die or to stop and to hand over the die to their opponent. The…

This paper studies the Best-of-K Bandit game: At each time the player chooses a subset S among all N-choose-K possible options and observes reward max(X(i) : i in S) where X is a random vector drawn from a joint distribution. The objective…

We study the distribution regression problem assuming the distribution of distributions has a doubling measure larger than one. First, we explore the geometry of any distributions that has doubling measure larger than one and build a small…

Moves in chess games are usually analyzed on a case-by-case basis by professional players, but thanks to the availability of large game databases, we can envision another approach of the game. Here, we indeed adopt a very different point of…

In this paper, we consider two-player zero-sum matrix and stochastic games and develop learning dynamics that are payoff-based, convergent, rational, and symmetric between the two players. Specifically, the learning dynamics for matrix…

Many people have flipped coins but few have stopped to ponder the statistical and physical intricacies of the process. We collected $350{,}757$ coin flips to test the counterintuitive prediction from a physics model of human coin tossing…

Machine learning relies on the assumption that unseen test instances of a classification problem follow the same distribution as observed training data. However, this principle can break down when machine learning is used to make important…

We propose a notion of a stable partition in a coalitional game that is parametrized by the concept of a defection function. This function assigns to each partition of the grand coalition a set of different coalition arrangements for a…

We study the problem of learning a most biased coin among a set of coins by tossing the coins adaptively. The goal is to minimize the number of tosses until we identify a coin i* whose posterior probability of being most biased is at least…

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…