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We study the complexity of a particular class of board games, which we call `slide and merge' games. Namely, we consider 2048 and Threes, which are among the most popular games of their type. In both games, the player is required to slide…

Computational Complexity · Computer Science 2015-01-19 Ahmed Abdelkader , Aditya Acharya , Philip Dasler

Risk is a well-known turn based board game where the primary objective is nothing less than the world domination. Gameplay is based on battles between armies located in adjacent territories on the map of Earth. The combat's outcome is…

Computer Science and Game Theory · Computer Science 2012-04-19 Manu Harju

We study the Levine hat problem, a cooperative puzzle introduced by Lionel Levine in 2010, in which $n \geq 2$ players must simultaneously identify a black hat on their own infinite stack, each seeing only their teammates' stacks. While the…

Combinatorics · Mathematics 2026-04-21 Clément Bouquet , Salah Chikhi , Timothé Charles , Yanghao Zhou , Eric Wang

In dynamic games with asymmetric information structure, the widely used concept of equilibrium is perfect Bayesian equilibrium (PBE). This is expressed as a strategy and belief pair that simultaneously satisfy sequential rationality and…

Computer Science and Game Theory · Computer Science 2016-09-15 Abhinav Sinha , Achilleas Anastasopoulos

The game of best choice (also known as the secretary problem) is a model for sequential decision making with a long history and many variations. The classical setup assumes that the sequence of candidate rankings are uniformly distributed.…

Combinatorics · Mathematics 2019-11-06 Brant Jones

We consider a multi-player non-zero-sum turn-based game (abbreviated as multi-player game) on a finite directed graph. A secure equilibrium (SE) is a strategy profile in which no player has the incentive to deviate from the strategy because…

Computer Science and Game Theory · Computer Science 2025-09-03 Hiroki Mizuno , Yoshiaki Takata , Hiroyuki Seki

Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…

Computer Science and Game Theory · Computer Science 2011-11-22 Adam O. Kalinich

We consider a finite horizon repeated game with $N$ selfish players who observe their types privately and take actions, which are publicly observed. Their actions and types jointly determine their instantaneous rewards. In each period,…

Computer Science and Game Theory · Computer Science 2019-05-17 Deepanshu Vasal

We study a two-player game played on undirected graphs called {\sc Trail Trap}, which is a variant of a game known as {\sc Partizan Edge Geography}. One player starts by choosing any edge and moving a token from one endpoint to the other;…

Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world…

Artificial Intelligence · Computer Science 2018-08-01 Giuseppe De Nittis , Alberto Marchesi , Nicola Gatti

In the video game "7 Billion Humans", the player is requested to direct a group of workers to various destinations by writing a program that is executed simultaneously on each worker. While the game is quite rich and, indeed, it is…

Computational Complexity · Computer Science 2024-07-11 Alessandro Panconesi , Pietro Maria Posta , Mirko Giacchini

In this paper we study a cooperative card game called Hanabi from the viewpoint of algorithmic combinatorial game theory. In Hanabi, each card has one among $c$ colors and a number between $1$ and $n$. The aim is to make, for each color, a…

Discrete Mathematics · Computer Science 2017-03-09 Jean-Francois Baffier , Man-Kwun Chiu , Yago Diez , Matias Korman , Valia Mitsou , André van Renssen , Marcel Roeloffzen , Yushi Uno

We quantized the Hawk-Dove game by using the most general form of a pure initial state to investigate the existence of pure and mixed Evolutionarily Stable Strategies (ESS). An example is considered to draw a comparison between classical…

Quantum Physics · Physics 2010-12-23 Ahmad Nawaz , A. H. Toor

We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability $p_{F}$ for the existence of Maker's strategy to claim a member of $F$ in the unbiased game played on…

Combinatorics · Mathematics 2007-05-23 Milos Stojakovic , Tibor Szabo

Adversarial environments require agents to navigate a key strategic trade-off: acquiring information enhances situational awareness, but may simultaneously expose them to threats. To investigate this tension, we formulate a…

Artificial Intelligence · Computer Science 2025-10-10 Valerio La Gatta , Dolev Mutzari , Sarit Kraus , VS Subrahmanian

Abalone is a 2-player board game with perfect information. The game is played on a 5x5x5 hexagonal grid and ends when a player pushes 6 of their opponents' pieces off the board. Abalone is similar to games like chess and Go in that all…

Combinatorics · Mathematics 2023-08-08 Joseph Gutstadt , Kirsten Hogenson , John Koerner

The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation…

Computer Science and Game Theory · Computer Science 2025-02-07 Oliver Biggar , Iman Shames

Finite-horizon probabilistic multiagent concurrent game systems, also known as finite multiplayer stochastic games, are a well-studied model in computer science due to their ability to represent a wide range of real-world scenarios…

Computer Science and Game Theory · Computer Science 2026-05-27 Senthil Rajasekaran , Moshe Y. Vardi

A partially parallel dynamical noisy binary choice (Ising) game in discrete time of $N$ players on complete graphs with $k$ players having a possibility of changing their strategies at each time moment called $k$-flip Ising game is…

Computer Science and Game Theory · Computer Science 2025-12-12 Kovalenko Aleksandr , Andrey Leonidov

$\textit{Magic: The Gathering}$ is a popular and famously complicated trading card game about magical combat. In this paper we show that optimal play in real-world $\textit{Magic}$ is at least as hard as the Halting Problem, solving a…

Artificial Intelligence · Computer Science 2019-04-24 Alex Churchill , Stella Biderman , Austin Herrick