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Chess has long been a testbed for AI's quest to match human intelligence, and in recent years, chess AI systems have surpassed the strongest humans at the game. However, these systems are not human-aligned; they are unable to match the…
Here we introduce a model in which individuals differ in the rate at which they seek new interactions with others, making rational decisions modeled as general symmetric two-player games. Once a link between two individuals has formed, the…
We investigate the probability distribution of order imbalance calculated from the order flow data of 43 Chinese stocks traded on the Shenzhen Stock Exchange. Two definitions of order imbalance are considered based on the order number and…
Tic Tac Toe is amongst the most well-known games. It has already been shown that it is a biased game, giving more chances to win for the first player leaving only a draw or a loss as possibilities for the opponent, assuming both the players…
In this paper, the rules of Niel's Chess are adapted to the game of Xiangqi, following the idea that the River and the Palaces play an important role in restricting and enabling chess pieces in their movements.
The frequencies at which individual words occur across languages follow power law distributions, a pattern of findings known as Zipf's law. A vast literature argues over whether this serves to optimize the efficiency of human communication,…
Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical…
Power law distribution is common in real-world networks including online social networks. Many studies on complex networks focus on the characteristics of vertices, which are always proved to follow the power law. However, few researches…
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…
Zipf's law has been found in many human-related fields, including language, where the frequency of a word is persistently found as a power law function of its frequency rank, known as Zipf's law. However, there is much dispute whether it is…
The study of linear-quadratic stochastic differential games on directed networks was initiated in Feng, Fouque \& Ichiba \cite{fengFouqueIchiba2020linearquadratic}. In that work, the game on a directed chain with finite or infinite players…
The binary many-step Markov chain with the step-like memory function is considered as a model for the analysis of rank distributions of words in stochastic symbolic dynamical systems. We prove that the envelope curve for this distribution…
We continue our studies of burn-off chip-firing games from [Discrete Math. Theor. Comput. Sci. 15 (2013), no. 1, 121-132; MR3040546] and [Australas. J. Combin. 68 (2017), no. 3, 330-345; MR3656659]. The latter article introduced randomness…
In the Korean traditional board game Yut-Nori, teams compete by moving their pieces on the two-dimensional game board, and the team whose all pieces complete a round trip on the board wins. In every round, teams throw four wooden sticks of…
We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statistics
We consider a family of distributions on which natural tail orders can be constructed upon a representation of a distribution by a (single) hyper-real number. Past research revealed that the ordering can herein strongly depend on the…
There is convincing evidence showing that the probability distributions of stock returns in mature markets exhibit power-law tails and both the positive and negative tails conform to the inverse cubic law. It supports the possibility that…
An active line of research has considered games played on networks in which payoffs depend on both a player's individual decision and also the decisions of her neighbors. Such games have been used to model issues including the formation of…
The intellectual property protection system constructed by China's Foreign Investment Law has opened a new phase of rule of law protection of intellectual property rights for foreign-invested enterprises, which is an important institutional…
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear…