相关论文: Weiqi games as a tree: Zipf's law of openings and …
The Weihrauch degrees and strong Weihrauch degrees are partially ordered structures representing degrees of unsolvability of various mathematical problems. Their study has been widely applied in computable analysis, complexity theory, and…
The game Arc-Kayles is played on an undirected graph with two players taking turns deleting an edge and its endpoints from the graph. We study a generalization of this game, Weighted Arc Kayles (WAK for short), played on graphs with…
The Zipf distribution also known as scale-free distribution or discrete Pareto distribution, is the particular case of Power Law distribution with support the strictly positive integers. It is a one-parameter distribution with a linear…
Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties and…
Consider a rooted Galton-Watson tree $T$, to each of whose edges we assign, independently, a weight that equals $+1$ with probability $p_{1}$, $0$ with probability $p_{0}$ and $-1$ with probability $p_{-1}=1-p_{1}-p_{0}$. We play a game on…
We study the complexity of computing equilibria in binary public goods games on undirected graphs. In such a game, players correspond to vertices in a graph and face a binary choice of performing an action, or not. Each player's decision…
Modern board games are a rich source of entertainment for many people, but also contain interesting and challenging structures for game playing research and implementing game playing agents. This paper studies the game Patchwork, a two…
Suppose some cleverness score parameter is sufficiently interesting to be defined and then measured, perhaps for different strata of specialists or for the broader population. Such phenomena could have Gaussian distributions, when it comes…
The Swiss-system is an increasingly popular competition format as it provides a favourable trade-off between the number of matches and ranking accuracy. However, there is no empirical study on the potential unfairness of Swiss-system chess…
We introduce and analyze the ordered Zeckendorf game, a novel combinatorial two-player game inspired by Zeckendorf's Theorem, which guarantees a unique decomposition of every positive integer as a sum of non-consecutive Fibonacci numbers.…
Leaves, i.e., vertices of degree one, can play a significant role in graph structure, especially in sparsely connected settings in which leaves often constitute the largest fraction of vertices. We consider a leaf-based counterpart of the…
A common format for sports contests involves pairwise matches between two teams, with the #1 player of team A matched against the #1 player of team B, the #2 player of team A against the #2 player of team B, and so on. This paper addresses…
Mobile games have gained immense popularity due to their accessibility, allowing people to play anywhere, anytime. Dark patterns and deceptive designs (DPs) have been found in these and other gaming platforms within certain cultural…
Previous research has highlighted the importance of strong heterogeneity for the successful evolution of cooperation in games governed by pairwise interactions. Here we determine to what extent this is true for games governed by group…
Positional games are a mathematical class of two-player games comprising Tic-tac-toe and its generalizations. We propose a novel encoding of these games into Quantified Boolean Formulas (QBFs) such that a game instance admits a winning…
We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…
Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says "Heads" or "Tails". The team wins if all four choices match; otherwise the Devil wins. If all team…
This paper proposes a new mechanism for pruning a search game-tree in computer chess. The algorithm stores and then reuses chains or sequences of moves, built up from previous searches. These move sequences have a built-in forward-pruning…
We demonstrate that large texts, representing human (English, Russian, Ukrainian) and artificial (C++, Java) languages, display quantitative patterns characterized by the Benford-like and Zipf laws. The frequency of a word following the…
Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result, though with a different notion of a legal decomposition, holds for many other sequences. We use these…