相关论文: The Value of Chess Squares
Modern chess engines significantly outperform human players and are essential for evaluating positions and move quality. These engines assign a numerical evaluation $E$ to positions, indicating an advantage for either white or black, but…
Archaeologists are in dire need of automated object reconstruction methods. Fragments reassembly is close to puzzle problems, which may be solved by computer vision algorithms. As they are often beaten on most image related tasks by deep…
Individuals, or organizations, cooperate with or compete against one another in a wide range of practical situations. Such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only…
The article describes a model of chess based on information theory. A mathematical model of the partial depth scheme is outlined and a formula for the partial depth added for each ply is calculated from the principles of the model. An…
We describe a general method of detecting valid chains or links of pieces on a two-dimensional grid. Specifically, using the example of the chess variant known as Switch-Side Chain-Chess (SSCC). Presently, no foolproof method of detecting…
In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…
In this dissertation, we analyze the computational properties of game-theoretic centrality measures. The key idea behind game-theoretic approach to network analysis is to treat nodes as players in a cooperative game, where the value of each…
We study the computation of approximate pure Nash equilibria in Shapley value (SV) weighted congestion games, introduced in [19]. This class of games considers weighted congestion games in which Shapley values are used as an alternative (to…
In imperfect information games, the game state is generally not fully observable to players. Therefore, good gameplay requires policies that deal with the different information that is hidden from each player. To combat this, effective…
The Shapley value is a common tool in game theory to evaluate the importance of a player in a cooperative setting. In a geometric context, it provides a way to measure the contribution of a geometric object in a set towards some function on…
A combinatorial game is a two-player game without hidden information or chance elements. One of the major approaches to analyzing games in combinatorial game theory is to break down a given game position into a disjunctive sum of multiple…
A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…
When defining the amount of additive structure on a set it is often convenient to consider certain sumsets; Calculating the cardinality of these sumsets can elucidate the set's underlying structure. We begin by investigating finite sets of…
AI engines utilizing deep learning neural networks provide excellent tools for analyzing traditional board games. Here we are interested in gaining new insights into the ancient game of Go. For that purpose, we need to define new numerical…
The number of ways to place $q$ nonattacking queens, bishops, or similar chess pieces on an $n\times n$ square chessboard is essentially a quasipolynomial function of $n$ (by Part I of this series). The period of the quasipolynomial is…
In artificial neural networks, understanding the contributions of input features on the prediction fosters model explainability and delivers relevant information about the dataset. While typical setups for feature importance ranking assess…
In Briata, Dall'Aglio and Fragnelli (2012), the authors introduce a cooperative game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in the fair division procedure introduced by…
By means of the Ehrhart theory of inside-out polytopes we establish a general counting theory for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen, on a polygonal convex board. The number of ways…
Options have provided a field of much study because of the complexity involved in pricing them. The Black-Scholes equations were developed to price options but they are only valid for European styled options. There is added complexity when…
A famous (and hard) chess problem asks what is the maximum number of safe squares possible in placing $n$ queens on an $n\times n$ board. We examine related problems from placing $n$ rooks. We prove that as $n\to\infty$, the probability…