Related papers: The Value of Chess Squares
Solving parity games is a major building block for numerous applications in reactive program verification and synthesis. While they can be solved efficiently in practice, no known approach has a polynomial worst-case runtime complexity. We…
The legal positions of a strong placement game, such as Domineering, form a simplicial complex called the legal complex. In this paper, we use the legal complex to study the game values taken on by the class of strong placement games using…
Can players sustain long-run trust when their equilibrium beliefs are shaped by machine-learning methods that penalize complexity? I study a game in which an infinite sequence of agents with one-period recall decides whether to place trust…
Gambits are central to human decision-making. Our goal is to provide a theory of Gambits. A Gambit is a combination of psychological and technical factors designed to disrupt predictable play. Chess provides an environment to study gambits…
This work focuses on the analysis of Chess 960, also known as Fischer Random Chess, a variant of traditional chess where the starting positions of the pieces are randomized. The study aims to predict the game outcome using machine learning…
In this paper we apply model predictive control (MPC), rollout, and reinforcement learning (RL) methodologies to computer chess. We introduce a new architecture for move selection, within which available chess engines are used as…
Shapley value is originally a concept in econometrics to fairly distribute both gains and costs to players in a coalition game. In the recent decades, its application has been extended to other areas such as marketing, engineering and…
A chain is an ordering of the integers 1 to n such that adjacent pairs have sums of a particular form, such as squares, cubes, triangular numbers, pentagonal numbers, or Fibonacci numbers. For example 4 1 2 3 5 form a Fibonacci chain while…
We explain how the prototype automatic chess problem composer, Chesthetica, successfully composed a rare and interesting chess problem using the new Digital Synaptic Neural Substrate (DSNS) computational creativity approach. This problem…
Powerful artificial intelligence systems are often used in settings where they must interact with agents that are computationally much weaker, for example when they work alongside humans or operate in complex environments where some tasks…
This study introduces the \emph{edge-based Shapley value}, a novel allocation rule within cooperative game theory, specifically tailored for networked systems, where value is generated through interactions represented by edges. Traditional…
In a combinatorial exchange setting, players place sell (resp. buy) bids on combinations of traded goods. Besides the question of finding an optimal selection of winning bids, the question of how to share the obtained profit is of high…
In this paper, we study the problem of evaluating the addition of elements to a set. This problem is difficult, because it can, in the general case, not be reduced to unconditional preferences between the choices. Therefore, we model…
Variational quantum algorithms (VQAs) offer a promising near-term approach to finding optimal quantum strategies for playing non-local games. These games test quantum correlations beyond classical limits and enable entanglement…
We present here the new insight or revisiting the algorithm for playing in Chess with incomplete information (which can be recognized by its newly short-name as Phoenix-Chess strategy). The only difference with respect to the classical…
Mastering games is a hard task, as games can be extremely complex, and still fundamentally different in structure from one another. While the AlphaZero algorithm has demonstrated an impressive ability to learn the rules and strategy of a…
We consider the problem of ranking $N$ objects starting from a set of noisy pairwise comparisons provided by a crowd of equal workers. We assume that objects are endowed with intrinsic qualities and that the probability with which an object…
We generalize Rock Paper Scissors to complete directed graphs, or tournaments, on $n$ vertices. Properties of the mixed-strategy Nash equilibria of these tournaments are discussed, particularly those with Nash equilibria where all of the…
We investigate the application of the Shapley value to quantifying the contribution of a tuple to a query answer. The Shapley value is a widely known numerical measure in cooperative game theory and in many applications of game theory for…
The field of deep learning has seen significant advancement in recent years. However, much of the existing work has been focused on real-valued numbers. Recent work has shown that a deep learning system using the complex numbers can be…