相关论文: JiangJun: Mastering Xiangqi by Tackling Non-Transi…

We provide two methodologies in the area of computation theory to solve optimal strategies for board games such as Xi Gua Qi and Go. From experimental results, we find relevance to graph theory, matrix representation, and mathematical…

Two-player complete-information game trees are perhaps the simplest possible setting for studying general-sum games and the computational problem of finding equilibria. These games admit a simple bottom-up algorithm for finding subgame…

This paper provides a complexity analysis for the game of dark Chinese chess (a.k.a. "JieQi"), a variation of Chinese chess. Dark Chinese chess combines some of the most complicated aspects of board and card games, such as long-term…

We have developed a high-performance Chinese Chess AI that operates without reliance on search algorithms. This AI has demonstrated the capability to compete at a level commensurate with the top 0.1\% of human players. By eliminating the…

Zero-sum games such as chess and poker are, abstractly, functions that evaluate pairs of agents, for example labeling them `winner' and `loser'. If the game is approximately transitive, then self-play generates sequences of agents of…

The game of Chinese Checkers is a challenging traditional board game of perfect information that differs from other traditional games in two main aspects: first, unlike Chess, all checkers remain indefinitely in the game and hence the…

In this paper, we investigate a class of nonzero-sum dynamic stochastic games, where players have linear dynamics and quadratic cost functions. The players are coupled in both dynamics and cost through a linear regression (weighted average)…

Monte Carlo Tree Search (MCTS) has recently been successfully used to create strategies for playing imperfect-information games. Despite its popularity, there are no theoretic results that guarantee its convergence to a well-defined…

We study 2-player zero-sum concurrent (i.e., simultaneous move) stochastic B\"uchi games and Transience games on countable graphs. Two players, Max and Min, seek respectively to maximize and minimize the probability of satisfying the game…

It has long been believed that Chess is the \emph{Drosophila} of Artificial Intelligence (AI). Studying Chess can productively provide valid knowledge about complex systems. Although remarkable progress has been made on solving Chess, the…

The advancement of data-driven artificial intelligence (AI), particularly machine learning, heavily depends on large-scale benchmarks. Despite remarkable progress across domains ranging from pattern recognition to intelligent…

A distributed Nash equilibrium seeking algorithm is presented for networked games. We assume an incomplete information available to each player about the other players' actions. The players communicate over a strongly connected digraph to…

We broaden the basis of non-cooperative game theory by considering miscoordination on a solution concept. For any solution concept, we extend the solution set of a strategic-form game to a transition set. This set contains profiles where…

Strategic randomization is a key principle in game theory, yet it remains underexplored in large language models (LLMs). Prior work often conflates the cognitive decision to randomize with the mechanical generation of randomness, leading to…

In this paper, we introduce an innovative deep learning architecture, termed Xiangqi Structurally Variable (XQSV), designed to emulate the behavioral patterns of human players in Xiangqi, or Chinese Chess. The unique attribute of XQSV is…

In this paper, we first devise two algorithms to determine whether or not a bimatrix game has a strategically equivalent zero-sum game. If so, we propose an algorithm that computes the strategically equivalent zero-sum game. If a given…

We study Monte Carlo tree search (MCTS) in zero-sum extensive-form games with perfect information and simultaneous moves. We present a general template of MCTS algorithms for these games, which can be instantiated by various selection…

We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum…

Game playing has long served as a fundamental benchmark for evaluating Artificial General Intelligence. While Large Language Models (LLMs) have demonstrated impressive capabilities in general reasoning, their effectiveness in spatial…

This paper addresses the distributed Nash Equilibrium seeking problem for aggregative games, where legitimate players' decisions are affected by potential malicious players. To describe players' behavior, we introduce a novel heterogeneous…