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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

Reachability games are two-player games played on a graph, where the objective of $\texttt{REACH}$ player is to reach the target set whereas the objective of $\texttt{SAFE}$ player is to stay away from the target set. Reachability games…

Artificial Intelligence · Computer Science 2026-05-12 Krishnendu Chatterjee , Ehsan Kafshdar Goharshady , Mehrdad Karrabi , Maximilian Seeliger , Đorđe Žikelić

The New York Times (NYT) games have found widespread popularity in recent years and reportedly account for an increasing fraction of the newspaper's readership. In this paper, we bring the computational lens to the study of New York Times…

Computational Complexity · Computer Science 2025-09-16 Alessandro Giovanni Alberti , Flavio Chierichetti , Mirko Giacchini , Daniele Muscillo , Alessandro Panconesi , Erasmo Tani

We completely classify winning strategies in the Ideal Chomp Game played on $\bar{K}$-algebras R of rank at most 6. In this two-player combinatorial game, players alternately add generators to build an ideal inside a given ring R, with the…

Combinatorics · Mathematics 2025-11-04 Leopold Karl

Nim is a well-known combinatorial game in which two players alternately remove stones from distinct piles. A player who removes the last stone wins under the normal play rule, while a player loses under the mis\`ere play rule. In this…

Combinatorics · Mathematics 2026-03-10 Hiromi Oginuma , Masato Shinoda

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…

Discrete Mathematics · Computer Science 2018-01-12 Ulrich Pferschy , Gaia Nicosia , Andrea Pacifici

The theory of combinatorial game (like board games) and the theory of social games (where one looks for Nash equilibria) are normally considered as two separate theories. Here we shall see what comes out of combining the ideas. The central…

Probability · Mathematics 2010-05-28 Peter Harremoes

An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an…

Computer Science and Game Theory · Computer Science 2013-08-01 Leslie Ann Goldberg , Paul W. Goldberg , Piotr Krysta , Carmine Ventre

The Poison Game is a two-player game played on a graph in which one player can influence which edges the other player is able to traverse. It operationalizes the notion of existence of credulously admissible sets in an argumentation…

Logic in Computer Science · Computer Science 2019-02-20 Davide Grossi , Simon Rey

We introduce a variant of Wythoff's Game that we call $m$-Modular Wythoff's Game. In the original Wythoff's Game, players can take a positive number of tokens from one pile, or they can take a positive number of tokens from both piles if…

Combinatorics · Mathematics 2024-02-22 Tanya Khovanova , Shuheng Niu

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

Optimization and Control · Mathematics 2008-06-17 Parikshit Shah , Pablo A. Parrilo

The class of passable games was recently introduced by Selinger as a class of combinatorial games that are suitable for modelling monotone set coloring games such as Hex. In a monotone set coloring game, the players alternately color the…

Combinatorics · Mathematics 2025-06-03 Eric Demer , Peter Selinger , Kyle Wang

We derive multiparty games that, if the winning chance exceeds a certain limit, prove the incompatibility of the parties' causal relations with any partial order. This, in turn, means that the parties exert a back-action on the causal…

General Relativity and Quantum Cosmology · Physics 2025-05-15 Eleftherios-Ermis Tselentis , Ämin Baumeler

We introduce and analyze the ordered Zeckendorf game, a novel combinatorial two-player game inspired by Zeckendorf's Theorem, which guarantees a unique decomposition of every positive integer as a sum of non-consecutive Fibonacci numbers.…

Number Theory · Mathematics 2026-03-31 Ivan Bortnovskyi , Michael Lucas , Steven J. Miller , Iana Vranesko , Ren Watson , Cameron White

Dots-and-Boxes is a popular children's game whose winning strategies have been studied by Berlekamp, Conway, Guy, and others. In this article we consider two variations, Dots-and-Triangles and Dots-and-Polygons, both of which utilize the…

History and Overview · Mathematics 2020-12-21 Jessica Dickson , Rachel Perrier

We introduce perfect half space games, in which the goal of Player 2 is to make the sums of encountered multi-dimensional weights diverge in a direction which is consistent with a chosen sequence of perfect half spaces (chosen dynamically…

Computer Science and Game Theory · Computer Science 2019-08-20 Thomas Colcombet , Marcin Jurdziński , Ranko Lazić , Sylvain Schmitz

In this paper we study a variant of the solitaire game Lights-Out, where the player's goal is to turn off a grid of lights. This variant is a two-player impartial game where the goal is to make the final valid move. This version is playable…

Combinatorics · Mathematics 2024-11-14 Eugene Fiorini , Maxwell Fogler , Katherine Levandosky , Bryan Lu , Jacob Porter , Andrew Woldar

Finding a counterfeit coin with the different weight from a set of visually identical coin using a balance, usually a two-armed balance, known as the balance question, is an intersting and inspiring question. Its variants involve…

Information Theory · Computer Science 2020-07-28 Fangqi Li

In this paper we introduce polytopal stochastic games, an extension of two-player, zero-sum, turn-based stochastic games, in which we may have uncertainty over the transition probabilities. In these games the uncertainty over the…

Logic in Computer Science · Computer Science 2025-02-26 Pablo F. Castro , Pedro D'Argenio

We define and give results on the game NecklaceNim NN($n$,$k$) which is PathNim PN($n$,$k$) with an additional move allowed on the end vertices. This game arises as a sub-game in the context of solving CircularNim CN($n$,$k$) when $k-2$…

Combinatorics · Mathematics 2026-04-14 Balaji R. Kadam , Silvia Heubach , Matthieu Dufour