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We consider two games between two players Ann and Ben who build a word together by adding alternatively a letter at the end of the shared word. In the nonrepetitive game, Ben wins the game if he can create a square of length at least $4$,…

Combinatorics · Mathematics 2022-11-30 Matthieu Rosenfeld

Using mostly elementary considerations, we find out who wins the game of Domineering on all rectangular boards of width 2, 3, 5, and 7. We obtain bounds on other boards as well, and prove the existence of polynomial-time strategies for…

Combinatorics · Mathematics 2007-05-23 Michael Lachmann , Cristopher Moore , Ivan Rapaport

We introduce a graph Ramsey game called Ramsey, Paper, Scissors. This game has two players, Proposer and Decider. Starting from an empty graph on $n$ vertices, on each turn Proposer proposes a potential edge and Decider simultaneously…

Combinatorics · Mathematics 2020-06-24 Jacob Fox , Xiaoyu He , Yuval Wigderson

In this work we have introduced two party games with respective winning conditions. One cannot win these games deterministically in the classical world if they are not allowed to communicate at any stage of the game. Interestingly we find…

Quantum Physics · Physics 2008-11-19 Indranil Chakrabarty , B. S. Choudhury

We consider a game with two piles, in which two players take turn to add $a$ or $b$ chips ($a$, $b$ are not necessarily positive) randomly and independently to their respective piles. The player who collects $n$ chips first wins the game.…

Combinatorics · Mathematics 2019-03-11 Ho-Hon Leung , Thotsaporn "Aek'' Thanatipanonda

We consider the following cake cutting game: Alice chooses a set P of n points in the square (cake) [0,1]^2, where (0,0) is in P; Bob cuts out n axis-parallel rectangles with disjoint interiors, each of them having a point of P as the lower…

Computational Geometry · Computer Science 2011-04-04 Tobias Christ , Andrea Francke , Heidi Gebauer , Jiří Matoušek , Takeaki Uno

Political candidates often shift their positions opportunistically in hopes of capturing more votes. When there are only two candidates, the best strategy for each of them is often to move towards the other. This eventually results in two…

Dynamical Systems · Mathematics 2023-10-25 Christoph Börgers , Bruce Boghosian , Natasa Dragovic , Anna Haensch

Two players take turns claiming empty cells from an $n\times n$ grid. The first player (if any) to occupy a transversal (a set of $ n $ cells having no two cells in the same row or column) is the winner. What is the outcome of the game…

Combinatorics · Mathematics 2025-07-08 Žarko Ranđelović

The aim of this paper is to solve the "gift exchange" problem: you are one of n players, and there are n wrapped gifts on display; when your turn comes, you can either choose any of the remaining wrapped gifts, or you can "steal" a gift…

Combinatorics · Mathematics 2009-07-06 David Applegate , N. J. A. Sloane

Duality games are a way of looking at wave-particle duality. In these games. Alice and Bob together are playing against the House. The House specifies, at random, which of two sub-games Alice and Bob will play. One game, Ways, requires that…

Quantum Physics · Physics 2021-12-08 Mark Hillery

In the paper it is proven that the two-players turn-based stochastic game "Risk or Safety" has a unique solution. Both players need to play the same strategy if they want to maximize their winning chances. An analytical method based on the…

Combinatorics · Mathematics 2026-03-03 Rüdiger Jehn

We analyze a coin-based game with two players where, before starting the game, each player selects a string of length $n$ comprised of coin tosses. They alternate turns, choosing the outcome of a coin toss according to specific rules. As a…

Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play $\omega$ many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets…

Logic · Mathematics 2009-09-25 Marion Scheepers

The graph grabbing game is played on a non-negatively weighted connected graph by Alice and Bob who alternately claim a non-cut vertex from the remaining graph, where Alice plays first, to maximize the weights on their respective claimed…

Combinatorics · Mathematics 2020-07-24 Sopon Boriboon , Teeradej Kittipassorn

We have developed a program called MUDoS (Maastricht University Domineering Solver) that solves Domineering positions in a very efficient way. This enables the solution of known positions so far (up to the 10 x 10 board) much quicker…

Artificial Intelligence · Computer Science 2016-02-18 Jos W. H. M. Uiterwijk

In the game of Matching Pennies, Alice and Bob each hold a penny, and at every tick of the clock they simultaneously display the head or the tail sides of their coins. If they both display the same side, then Alice wins Bob's penny; if they…

Computer Science and Game Theory · Computer Science 2018-02-05 Dusko Pavlovic , Peter-Michael Seidel , Muzamil Yahia

In a seminal paper, Meyer [David Meyer, Phys. Rev. Lett. 82, 1052 (1999)] described the advantages of quantum game theory by looking at the classical penny flip game. A player using a quantum strategy can win against a classical player…

Quantum Physics · Physics 2015-10-29 Namit Anand , Colin Benjamin

Pseudo-telepathy provides an intuitive way of looking at Bell's inequalities, in which it is often obvious that feats achievable by use of quantum entanglement would be classically impossible. A two-player pseudo-telepathy game proceeds as…

Quantum Physics · Physics 2007-05-23 Gilles Brassard , Andre A. Methot , Alain Tapp

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…

Logic · Mathematics 2023-10-13 Ilkka Törmä

The $[X,Y]$-edge colouring game is played with a set of $k$ colours on a graph $G$ with initially uncoloured edges by two players, Alice (A) and Bob (B). The players move alternately. Player $X\in\{A,B\}$ has the first move.…

Combinatorics · Mathematics 2024-09-11 Stephan Dominique Andres , Wai Lam Fong