Related papers: Two-Color Babylon
We introduce a 2-player game played on an infinite grid, initially empty, where each player in turn chooses a vertex and colours it. The first player aims to create some pattern from a target set, while the second player aims to prevent it.…
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.…
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…
Let $a$, $b$, and $n$ be integers with $0<a<b<n$. In a certain two-player probabilistic chip-collecting game, Alice tosses a coin to determine whether she collects $a$ chips or $b$ chips. If Alice collects $a$ chips, then Bob collects $b$…
We introduce a two-player game, in which each player extends a given sequence by picking a free element in a domain D of the real line. The aim of the players is to control the parity of the number of transpositions necessary to put the…
Game coloring is a well-studied two-player game in which each player properly colors one vertex of a graph at a time until all the vertices are colored. An `eternal' version of game coloring is introduced in this paper in which the vertices…
We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group…
A protocol for considering decoherence in quantum games is presented. Results for two-player, two-strategy quantum games subject to decoherence are derived and some specific examples are given. Decoherence in other types of quantum games is…
We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem follows from a special case.
We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…
In this paper I shall clarify three cubic equations of Babylonian mathematics, whose solutions have not been fully explained; BM 85200, no.6 and no.7, and YBC 4669 B2.
We consider games with two antagonistic players --- \'Elo\"ise (modelling a program) and Ab\'elard (modelling a byzantine environment) --- and a third, unpredictable and uncontrollable player, that we call Nature. Motivated by the fact that…
The Game of Poker Chips, Dominoes and Survival fosters team building and high level cooperation in large groups, and is a tool applied in management training exercises. Each player, initially given two colored poker chips, is allowed to…
The angel-devil game is played on an infinite two-dimensional ``chessboard''. The squares of the board are all white at the beginning. The players called angel and devil take turns in their steps. When it is the devil's turn, he can turn a…
We study infinite two-player games where one of the players is unsure about the set of moves available to the other player. In particular, the set of moves of the other player is a strict superset of what she assumes it to be. We explore…
We consider the graph coloring game, a game in which two players take turns properly coloring the vertices of a graph, with one player attempting to complete a proper coloring, and the other player attempting to prevent a proper coloring.…
Two players play a game by alternately splitting a surface of a compact $2$-manifold along a simple closed curve that is not null-homotopic and attaching disks to the resulting boundary; the last player who can move wins. Starting from an…
We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…
In this paper we find viscosity solutions to the two membranes problem (that is a system with two obstacle-type equations) with two different $p-$Laplacian operators taking limits of value functions of a sequence of games. We analyze…
We investigate a multi-player and multi-choice quantum game. We start from two-player and two-choice game and the result is better than its classical version. Then we extend it to N-player and N-choice cases. In the quantum domain, we…