Related papers: The Complexity of Rummikub Problems
Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game ruleset. The problem is rephrased as determining the winner of the game where two opposing players take turns assigning values to boolean variables. In this…
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…
The 15 puzzle is a classic reconfiguration puzzle with fifteen uniquely labeled unit squares within a $4 \times 4$ board in which the goal is to slide the squares (without ever overlapping) into a target configuration. By generalizing the…
We report the results of a game-theoretic experiment with human players who solve the problems of increasing complexity by cooperating in groups of increasing size. Our experimental environment is set up to make it complicated for players…
Fibonacci nim is a popular impartial combinatorial game, usually played with a single pile of stones. The game is appealing due to its surprising connections with the Fibonacci numbers and the Zeckendorf representation. In this article, we…
We present a new tool for the study of multiplayer stochastic games, namely the modified game, which is a normal-form game that depends on the discount factor, the initial state, and for every player a partition of the set of states and a…
This paper presents a data-driven statistical framework to quantify the role of skill in games, addressing the long-standing question of whether success in a game is predominantly driven by skill or chance. We analyze player level data from…
Given a tiling of a 2D grid with several types of tiles, we can count for every row and column how many tiles of each type it intersects. These numbers are called the_projections_. We are interested in the problem of reconstructing a tiling…
Consider the following game between a random player R and a deterministic player D. There is a pile of n elements at the beginning. The rules for playing are as follows: In each turn of R, if the pile contains exactly m elements, R removes…
Games potentially provide a wealth of knowledge about our shared cultural past and the development of human civilisation, but our understanding of early games is incomplete and often based on unreliable reconstructions. This paper describes…
This contribution deals with a two-level discrete decision problem, a so-called Stackelberg strategic game: A Subset Sum setting is addressed with a set $N$ of items with given integer weights. One distinguished player, the leader, may…
We introduce and study Minkowski games. These are two player games, where the players take turns to chose positions in $\mathbb{R}^d$ based on some rules. Variants include boundedness games, where one player wants to keep the positions…
We study the computational complexity of a perfect-information two-player game proposed by Aigner and Fromme. The game takes place on an undirected graph where n simultaneously moving cops attempt to capture a single robber, all moving at…
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…
All roads lead to Rome is the core idea of the puzzle game Roma. It is played on an $n \times n$ grid consisting of quadratic cells. Those cells are grouped into boxes of at most four neighboring cells and are either filled, or to be…
The present work consisted in developing a plateau game. There are the traditional ones (monopoly, cluedo, ect.) but those which interest us leave less place at the chance (luck) than to the strategy such that the chess game. Kallah is an…
In the gift exchange game there are n players and n wrapped gifts. When a player's number is called, that person can either choose one of the remaining wrapped gifts, or can "steal" a gift from someone who has already unwrapped it, subject…
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…
Given $k\ge 3$ heaps of tokens. The moves of the 2-player game introduced here are to either take a positive number of tokens from at most $k-1$ heaps, or to remove the {\sl same} positive number of tokens from all the $k$ heaps. We analyse…
Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, because they are widely…