Related papers: Variants of Wythoff's game translating its P-posit…

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…

Consider a rooted Galton-Watson tree $T$, to each of whose edges we assign, independently, a weight that equals $+1$ with probability $p_{1}$, $0$ with probability $p_{0}$ and $-1$ with probability $p_{-1}=1-p_{1}-p_{0}$. We play a game on…

Although mixed extensions of finite games always admit equilibria, this is not the case for countable games, the best-known example being Wald's pick-the-larger-integer game. Several authors have provided conditions for the existence of…

We generalize the results and conjectures of Tam\'{a}s Lengyel, showing that the \textsc{nim}-values of a large class of two-dimensional subtraction-transfer games are periodic. These are impartial, normal-play games with two piles of…

We introduce a natural variant of weighted voting games, which we refer to as k-Prize Weighted Voting Games. Such games consist of n players with weights, and k prizes, of possibly differing values. The players form coalitions, and the i-th…

The authors present formulas for the previous player's winning positions of two variants of restricted Nim. In both of these two games, there is one pile of stones, and in the first variant, we investigate the case that in k-th turn, you…

We introduce and analyze the ordered Zeckendorf game, a novel combinatorial two-player game inspired by Zeckendorf's Theorem, which guarantees a unique decomposition of every positive integer as a sum of non-consecutive Fibonacci numbers.…

Let $PW_S^1$ be the space of integrable functions on $\mathbb{R}$ whose Fourier transform vanishes outside $S$, where $S = [-\sigma,-\rho]\cup[\rho,\sigma]$, $0<\rho<\sigma$. In the case $\rho>\sigma/2$, we present a complete description of…

The Monty Hall puzzle has been solved and dissected in many ways, but always using probabilistic arguments, so it is considered a probability puzzle. In this paper the puzzle is set up as an orthodox statistical problem involving an unknown…

By analyzing the singularity of standard intertwining operators, we provide a new way to understand the explicit location of reducibility points of induced representations of two Speh representations for general linear groups over a p-adic…

We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different…

Given a hypergraph $\cH \subseteq 2^I \setminus \{\emptyset\}$ on the ground set $I = \{1, \ldots, n\}$, we assign to each $i \in I$ a nonnegative integer $x_i$, that is a pile of $x_i$ tokens, and consider the following generalization of…

Finding a counterfeit coin with the different weight from a set of visually identical coin using a balance, usually a two-armed balance, known as the balance question, is an intersting and inspiring question. Its variants involve…

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…

Weighted voting games apply to a wide variety of multi-agent settings. They enable the formalization of power indices which quantify the coalitional power of players. We take a novel approach to the study of the power of big vs.~small…

Weighted voting games are a popular class of coalitional games that are widely used to model real-life situations of decision-making. They can be applied, for instance, to analyze legislative processes in parliaments or voting in corporate…

We establish the first hardness results for the problem of computing the value of one-round games played by a verifier and a team of provers who can share quantum entanglement. In particular, we show that it is NP-hard to approximate within…

Weighted voting games are a well-known and useful class of succinctly representable simple games that have many real-world applications, e.g., to model collective decision-making in legislative bodies or shareholder voting. Among the…

In late May of 2014 I received an email from a colleague introducing to me a non-transitive game developed by Walter Penney. This paper explores this probability game from the perspective of a coin tossing game, and further discusses some…

We introduce the following variant of the Gale-Berlekamp switching game. Let $P$ be a set of n noncollinear points in the plane, each of them having weight $+1$ or $-1$. At each step, we pick a line $\ell$ passing through at least two…