Related papers: Multi-Dimensional Chocolate and Nim with a Pass

The following game in a similar formulation to Petri nets and chip-firing games is studied: Given a finite collection of baskets, each has an infinite number of balls of the same value. Initially, a ball from some basket is chosen to put on…

For decades it is known that Quantum Computers might serve as a tool to solve a very specific kind of problems that have long thought to be incalculable. Some of those problems are of a combinatorial nature, with the quantum advantage…

We introduce Multiplicative Modular Nim (MuM), a variant of Nim in which the traditional nim-sum is replaced by heap-size multiplication modulo m. We establish a complete theory for this game, beginning with a direct, Bouton-style analysis…

We present a new family of Nim games where the rules depend on a given `coloring' of the tokens, each token being either black or white. The rules are as in Nim with the restriction that a white token on top of each heap is not allowed. We…

Cooperative Parrondo's games on a regular two dimensional lattice are analyzed based on the computer simulations and on the discrete-time Markov chain model with exact transition probabilities. The paradox appears in the vicinity of the…

Here, we present a variant of Nim with two piles. In the first pile, we have stones with a weight of 1, and in the second pile, we have stones with a weight of -2. Two Players take turns to take stones from one of the piles, and the total…

In a Maker-Breaker game there are two players, Maker and Breaker, where Maker wins if they create a specified structure while Breaker wins if they prevent Maker from winning indefinitely. A $3$-term arithmetic progression, or $3$-AP, is a…

There are many combinatorial games in which a move can terminate the game, such as a checkmate in chess. These moves give rise to diverse situations that fall outside the scope of the classical normal play structure. To analyze these games,…

We consider the setting of repeated fair division between two players, denoted Alice and Bob, with private valuations over a cake. In each round, a new cake arrives, which is identical to the ones in previous rounds. Alice cuts the cake at…

We examine the advantages that quantum strategies afford in communication-limited games. Inspired by the card game blackjack, we focus on cooperative, two-party sequential games in which a single classical bit of communication is allowed…

This paper develops a unified framework for zero-sum games in which both the pure strategies and the payoff matrices contain complex-valued entries. By leveraging a linear isomorphism between complex and real vector spaces, we extend key…

We study a generalization of the Mermin-Peres magic square game to arbitrary rectangular dimensions. After exhibiting some general properties, these rectangular games are fully characterized in terms of their optimal win probabilities for…

We introduce a search game for two players played on a "scenario" consisting of a ground set together with a collection of feasible partitions. This general setting allows us to obtain new characterisations of many width parameters such as…

Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several…

Schmidt's game is generally used to deduce qualitative information about the Hausdorff dimensions of fractal sets and their intersections. However, one can also ask about quantitative versions of the properties of winning sets. In this…

We consider the problem of determining the minimum number of moves needed to solve a certain one-dimensional peg puzzle. Let N be a positive integer. The puzzle apparatus consists of a block with a single row of 2N+1 equally spaced holes…

Subtraction games are played with one or more heaps of tokens, with players taking turns removing from a single heap a number of tokens belonging to a specified subtraction set; the last player to move wins. We describe how to compute the…

Non-crossing knight's tours in 3-dimension is a new field of research. The author has shown its possibility in small cuboids and in cubes up to 8x8x8 size. It can also be extended to larger size cubes and cuboids. The author has achieved…

In this article we compute analytically the number of Nash Equilibria (NE) for a two-choice game played on a (circular) ladder graph with $2n$ players. We consider a set of games with generic payoff parameters, with the only requirement…

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…