Related papers: The $\star$-operator and Invariant Subtraction Gam…

We introduce CUT, the class of 2-player partition games. These are NIM type games, played on a finite number of heaps of beans. The rules are given by a set of positive integers, which specifies the number of allowed splits a player can…

We introduce and study pawn games, a class of two-player zero-sum turn-based graph games. A turn-based graph game proceeds by placing a token on an initial vertex, and whoever controls the vertex on which the token is located, chooses its…

Let $f: M \to M$ be a $C^{1+\theta}$-partially hyperbolic diffeomorphism. We introduce a type of modified Schmidt games which is induced by $f$ and played on any unstable manifold. Utilizing it we generalize some results of \cite{Wu} as…

We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these \emph{lattice games} can be made particularly efficient for octal games, which we generalize to…

In this paper, we consider a modular extension to the game of Nim, which we call $m$-Modular Nim, and explore its optimal strategy. In $m$-Modular Nim, a player can either make a standard Nim move or remove a multiple of $m$ tokens in…

Wythoff's game is a modification of the well-known game of ``nim." Wythoff's game, which does not resemble the Fibonacci sequence, has direct relation to the Golden ratio. We will explore the sequence behind this surprising relationship,…

Motivated by the success of domination games and by a variation of the coloring game called the indicated coloring game, we introduce a version of domination games called the indicated domination game. It is played on an arbitrary graph $G$…

We propose a variant of Nim, named StrNim. Whereas a position in Nim is a tuple of non-negative integers, that in StrNim is a string, a sequence of characters. In every turn, each player shrinks the string, by removing a substring repeating…

Given a finite set of positive integers, $A$, and starting with a heap of $n$ chips, Alice and Bob alternate turns and on each turn a player chooses $x\in A$ with $x$ smaller or equal than the current number of chips and subtract $x$ chips…

We investigate game-theoretic variants of cardinal invariants of the continuum. The invariants we treat are the reaping number $\mathfrak{r}$, the bounding number $\mathfrak{b}$, the dominating number $\mathfrak{d}$, and the additivity…

We show how the software Walnut can be used to obtain concise proofs of results concerning variants of the famous Wythoff game, in which blocking maneuvers or terminal positions are added, as discussed respectively by Larsson (2011) and…

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 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 combining the definition of a cardinal invariant and the notion of an infinite game. We focus on the splitting number $\mathfrak{s}$ since the corresponding cardinal invariants behave in an interesting way. We introduce three…

Given two finite sets of integers $S\subseteq\NNN\setminus\{0\}$ and $D\subseteq\NNN\setminus\{0,1\}$,the impartial combinatorial game $\IMARK(S,D)$ is played on a heap of tokens. From a heap of $n$ tokens, each player can moveeither to a…

In this note, we investigate combinatorial games where both players move randomly (each turn, independently selecting a legal move uniformly at random). In this model, we provide closed-form expressions for the expected number of turns in a…

Simple stochastic games are two-player zero-sum stochastic games with turn-based moves, perfect information, and reachability winning conditions. We present two new algorithms computing the values of simple stochastic games. Both of them…

In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric $N$-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other…

We study transfinite cut-and-choose games on $T_0$ spaces, introducing the {\em point-separating number} $ps(X)$ and the {\em set membership number} ${sm}(X)$ as the ordinal-valued invariants measuring the minimal length of a game in which…

We introduce and study Minkowski games. These are two player games, where the players take turns to chose positions in $\mathbb{R}^d$ based on some rules. Variants include boundedness games, where one player wants to keep the positions…