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The stable marriage problem, as addressed by Gale and Shapely [1] consists of providing a bipartite matching between n " boys " and n " girls "-each of whom have a totally ordered preference list over the other set-such that there exists no…
Given a graph G with n vertices and k players, each of which is placing a facility on one of the vertices of G, we define the score of the i'th player to be the number of vertices for which, among all players, the facility placed by the…
Recent large language models (LLMs) have shown strong reasoning capabilities. However, a critical question remains: do these models possess genuine strategic reasoning, or do they primarily excel at pattern recognition? To address this, we…
We introduce a quantitative framework for separating skill and chance in games by modeling them as complementary sources of control over stochastic decision trees. We define the Skill-Luck Index S(G) in [-1, 1] by decomposing game outcomes…
In many professons employees are rewarded according to their relative performance. Corresponding economy can be modeled by taking $N$ independent agents who gain from the market with a rate which depends on their current gain. We argue that…
We present an end-to-end learning method for chess, relying on deep neural networks. Without any a priori knowledge, in particular without any knowledge regarding the rules of chess, a deep neural network is trained using a combination of…
Guessing games for directed graphs were introduced by Riis for studying multiple unicast network coding problems. In a guessing game, the players toss generalised dice and can see some of the other outcomes depending on the structure of an…
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…
To obtain reliable results of expertise, which usually use individual and group expert pairwise comparisons, it is important to summarize (aggregate) expert estimates provided that they are sufficiently consistent. There are several ways to…
The study of cultural evolution benefits from detailed analysis of cultural transmission in specific human domains. Chess provides a platform for understanding the transmission of knowledge due to its active community of players, precise…
It is non-trivial to design engaging and balanced sets of game rules. Modern chess has evolved over centuries, but without a similar recourse to history, the consequences of rule changes to game dynamics are difficult to predict. AlphaZero…
There are an increasing number of domains in which artificial intelligence (AI) systems both surpass human ability and accurately model human behavior. This introduces the possibility of algorithmically-informed teaching in these domains…
In the sport of cricket, variations in a player's batting ability can usually be measured on one of two scales. Short-term changes in ability that are observed during a single innings, and long-term changes that are witnessed between…
It is noted that some unusual moves against a strong chess program greatly weaken its ability to see the serious targets of the game, and its whole level of play... It is suggested to create programs with different weaknesses in order to…
Chess provides an ideal testbed for evaluating the reasoning, modeling, and abstraction capabilities of large language models (LLMs), as it has well-defined structure and objective ground truth while admitting a wide spectrum of skill…
We have seen numerous machine learning methods tackle the game of chess over the years. However, one common element in these works is the necessity of a finely optimized look ahead algorithm. The particular interest of this research lies…
We consider a gossip approach for finding a Nash equilibrium in a distributed multi-player network game. We extend previous results on Nash equilibrium seeking to the case when the players' cost functions may be affected by the actions of…
Owning up to the authors' occasional mixed performances when playing darts we follow up on the ingenious work to determine the optimal aim to score high by Tibshirani et. al [JRS A 174, 213 (2011)] and expand on maximal expected reward…
The opening book is an important component of a chess engine, and thus computer chess programmers have been developing automated methods to improve the quality of their books. For chess, which has a very rich opening theory, large databases…
Gauging an individual's skill level is crucial, as it inherently shapes their behavior. Quantifying skill, however, is challenging because it is latent to the observed actions. To explore skill understanding in human behavior, we focus on…