Related papers: PRIMES STEP Plays Games
This document presents the rules of a tactical two-player board game which is inspired by spin glasses. The aim is, while placing bonds and spins, to achieve a majority of the spins facing the chosen direction of each player. The game has…
We study games with finitely many participants, each having finitely many choices. We consider the following categories of participants: (I) populations: sets of nonatomic agents, (II) atomic splittable players, (III) atomic non splittable…
Without further ado, we present the P_3-game. The P_3-game is decidable for elementary classes of graphs such as paths and cycles. From an algorithmic point of view, the connected P_3-game is fascinating. We show that the connected P_3-game…
Past efforts to classify impartial three-player combinatorial games (the theories of Li and Straffin) have made various restrictive assumptions about the rationality of one's opponents and the formation and behavior of coalitions. One may…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
We study a three-player variation of the impartial avoidance game introduced by Anderson and Harary. Three players take turns selecting previously-unselected elements of a finite group. The losing player is the one who selects an element…
Educators often seek ways to introduce gaming in the classroom in order to break the usual teaching routine, expand the usual course curriculum with additional knowledge, but mostly as a means to motivate students and increase their…
Aim: Present a systematic development of part of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of…
Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…
We study a game where two players take turns selecting points of a convex geometry until the convex closure of the jointly selected points contains all the points of a given winning set. The winner of the game is the last player able to…
We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…
Given $n$ piles of tokens and a positive integer $k \leq n$, we study the following two impartial combinatorial games Nim$^1_{n, \leq k}$ and Nim$^1_{n, =k}$. In the first (resp. second) game, a player, by one move, chooses at least $1$ and…
Assistance games (also known as cooperative inverse reinforcement learning games) have been proposed as a model for beneficial AI, wherein a robotic agent must act on behalf of a human principal but is initially uncertain about the humans…
This paper explores a PAC (probably approximately correct) learning model in cooperative games. Specifically, we are given $m$ random samples of coalitions and their values, taken from some unknown cooperative game; can we predict the…
We consider three variants of a partisan combinatorial game between two players, Left and Right, played on an undirected simple graph. Left is able to delete vertices (and incident edges) while Right is able to delete edges. This natural…
We study 2-player impartial games of the form take-away which produce P-positions (second player winning positions) corresponding to complementary Beatty sequences, given by the continued fractions (1;k,1,k,1,...) and (k+1;k,1,k,1,...). Our…
Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…
We describe a contest in variable selection which was part of a statistics course for graduate students. In particular, the possibility to create a contest themselves offered an additional challenge for more advanced students. Since working…
Procedures of the short-term predictions for processes in general 2-person differential interactive games are proposed. Their effectiveness is discussed.
A nationally representative study of video game play among adolescents in the United States showed that 97% of adolescents aged 12 to 17 years play computer, web, and portable (or console) video games (Lenhart et al., 2008). We hypothesized…