Related papers: Extended circular nim

This paper presents iNNK, a multiplayer drawing game where human players team up against an NN. The players need to successfully communicate a secret code word to each other through drawings, without being deciphered by the NN. With this…

This paper introduces a variant of the impartial combinatorial game nim, called tree nim, as well as a particular case of tree nim called tripod nim. A certain existence-uniqueness result and a periodicity result are proven about the…

We prove computational intractability of variants of checkers: (1) deciding whether there is a move that forces the other player to win in one move is NP-complete; (2) checkers where players must always be able to jump on their turn is…

Let T(m,n) denote the number of ways to tile an m-by-n rectangle with dominos. For any fixed m, the numbers T(m,n) satisfy a linear recurrence relation, and so may be extrapolated to negative values of n; these extrapolated values satisfy…

For a topological space $X$ and a point $x \in X$, consider the following game -- related to the property of $X$ being countably tight at $x$. In each inning $n\in\omega$, the first player chooses a set $A_n$ that clusters at $x$, and then…

In this paper we have used one 2 variable Boolean function called Rule 6 to define another beautiful transformation named as Extended Rule-6. Using this function we have explored the algebraic beauties and its application to an efficient…

A formal n-square is the set of positions in an square matrix of size n. A shuffle of a formal n-square consists of independent rotations of each row and of each column. A key result turns out to be valid at least for n <= 34 and n = 37:…

We study a modified prisoner's dilemma game taking place on two-dimensional disordered square lattices. The players are pure strategists and can either cooperate or defect with their immediate neighbors. In the generations each player…

Consider the following variant of Rock, Paper, Scissors (RPS) played by two players Rei and Norman. The game consists of $3n$ rounds of RPS, with the twist being that Rei (the restricted player) must use each of Rock, Paper, and Scissors…

We study the strategic considerations of miners participating in the bitcoin's protocol. We formulate and study the stochastic game that underlies these strategic considerations. The miners collectively build a tree of blocks, and they are…

We determine the full nim-value structure of additive subtraction games in the {\em primitive quadratic} regime. The problem appears in Winning Ways by Berlekamp et al. in 1982; it includes a closed formula, involving Beatty-type {\em…

Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result holds for other positive linear recurrence sequences. These legal decompositions can be used to…

We consider Subtraction Nim, where two players have exactly the same options, but which is partizan in the sense that at the game ending, a partizan rule is applied for the decision of the winner. We consider the following example: Let $S$…

We study the computational complexity of the popular board game backgammon. We show that deciding whether a player can win from a given board configuration is NP-Hard, PSPACE-Hard, and EXPTIME-Hard under different settings of known and…

The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…

We apply several quantization schemes to simple versions of the Chinos game. Classically, for two players with one coin each, there is a symmetric stable strategy that allows each player to win half of the times on average. A partial…

The Critical Node Problem (CNP) is to identify a subset of nodes in a graph whose removal maximally degrades pairwise connectivity. The CNP is an important variant of the Critical Node Detection Problem (CNDP) with wide applications. Due to…

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…

We consider random-turn positional games, introduced by Peres, Schramm, Sheffield and Wilson in 2007. A $p$-random-turn positional game is a two-player game, played the same as an ordinary positional game, except that instead of alternating…

We consider a multi-player non-zero-sum turn-based game (abbreviated as multi-player game) on a finite directed graph. A secure equilibrium (SE) is a strategy profile in which no player has the incentive to deviate from the strategy because…