Related papers: Battle Sheep is PSPACE-complete
This report presents Giraffe, a chess engine that uses self-play to discover all its domain-specific knowledge, with minimal hand-crafted knowledge given by the programmer. Unlike previous attempts using machine learning only to perform…
Hex is a well known connection game in which two players attempt to connect opposite sides of the board by colored stones. In 2022, Hamkins and Leonessi introduced an infinite version, in which the goal is to construct a certain kind of…
The Domination game is an impartial game on graphs, introduced in 2010, and proved PSPACE-complete in the normal variant in 2026. In this game, Alice and Bob alternately select playable vertices, where a vertex is playable if it dominates…
$\textit{Magic: The Gathering}$ 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…
Swish is a card game in which players are given cards having symbols (hoops and balls), and find a valid superposition of cards, called a "swish." Dailly, Lafourcade, and Marcadet (FUN 2024) studied a generalized version of Swish and showed…
Iterated coopetitive games capture the situation when one must efficiently balance between cooperation and competition with the other agents over time in order to win the game (e.g., to become the player with highest total utility).…
We present a new paradigm of games, i.e. SwarmPlay, where each playing component is presented by an individual drone that has its own mobility and swarm intelligence to win against a human player. The motivation behind the research is to…
In the classical Binary Networked Public Goods (BNPG) game, a player can either invest in a public project or decide not to invest. Based on the decisions of all the players, each player receives a reward as per his/her utility function.…
Bayesian game is a strategic decision-making model where each player's type parameter characterizing its own objective is private information: each player knows its own type but not its rivals' types, and Bayesian Nash equilibrium (BNE) is…
Perfect Bayesian Equilibrium (PBE) is a refinement of the Nash equilibrium for imperfect-information extensive-form games (EFGs) that enforces consistency between the two components of a solution: agents' strategy profile describing their…
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…
We consider the following two-player game: Maxi and Mini start with the empty graph on $n$ vertices and take turns, always adding one additional edge to the graph such that the chromatic number is at most $k$, where $k \in \mathbb{N}$ is a…
We consider a two-player game of war of attrition under complete information. It is well-known that this class of games admits equilibria in pure, as well as mixed strategies, and much of the literature has focused on the latter. We show…
We present a novel polynomial time approximation scheme for two-strategy anonymous games, in which the players' utility functions, although potentially different, do not differentiate among the identities of the other players. Our algorithm…
This paper investigates the popular card game UNO from the viewpoint of algorithmic combinatorial game theory. We define simple and concise mathematical models for the game, including both cooperative and uncooperative versions, and analyze…
The AB~Game is a game similar to the popular game Mastermind. We study a version of this game called Static Black-Peg AB~Game. It is played by two players, the codemaker and the codebreaker. The codemaker creates a so-called secret by…
2-TBSG is a two-player game model which aims to find Nash equilibriums and is widely utilized in reinforced learning and AI. Inspired by the fact that the simplex method for solving the deterministic discounted Markov decision processes…
Avoidance games are games in which two players claim vertices of a hypergraph and try to avoid some structures. These games are studied since the introduction of the game of SIM in 1968, but only few complexity results are known on them. In…
In this paper we study the computational complexity of computing an evolutionary stable strategy (ESS) in multi-player symmetric games. For two-player games, deciding existence of an ESS is complete for {\Sigma} 2 , the second level of the…
We propose and analyse a 2-parameter family of 2-player games on two heaps of tokens, and present a strategy based on a class of sequences. The strategy looks easy, but is actually hard. A class of exotic numeration systems is then used,…