Related papers: On Ending Partizan Subtraction Nim

The Lipschitz constant of a finite normal-form game is the maximal change in some player's payoff when a single opponent changes his strategy. We prove that games with small Lipschitz constant admit pure {\epsilon}-equilibria, and pinpoint…

Consider the following game between a random player R and a deterministic player D. There is a pile of n elements at the beginning. The rules for playing are as follows: In each turn of R, if the pile contains exactly m elements, R removes…

{\sc Yama Nim} is a variant of two piles {\sc Nim}. In this ruleset, the player chosses one of the piles and removes at least two tokens from the pile. In the same move, the player adds one token to the other pile. We show the winning…

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…

Toral introduced so-called cooperative Parrondo games, in which there are N players (3 or more) arranged in a circle. At each turn one player is randomly chosen to play. He plays either game A or game B, depending on the strategy. Game A…

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…

Consider concurrent, infinite duration, two-player win/lose games played on graphs. If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finite-memory) strategies is equivalent to the existence of…

Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers. We use this to create a two-player game. Given a fixed integer $n$ and an initial decomposition of $n = n F_1$, the two…

Losing a game is difficult. Recent work of Larsson, Nowakowski, and Santos, as well as that of Siegel, has opened up enticing lines of research into partizan mis\`ere theory. The algebraic structure of mis\`ere monoids is not yet well…

We introduce the notion of invariant vectors of a game and develop the Invariance Reduction Process, which first uses reduction of positions via invariance and then zero and merge reductions of games to arrive at smaller, solved sub-games…

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 consider zero-sum stochastic games with perfect information and finitely many states and actions. The payoff is computed by a function which associates to each infinite sequence of states and actions a real number. We prove that if the…

A poset game is a two-player game played over a partially ordered set (poset) in which the players alternate choosing an element of the poset, removing it and all elements greater than it. The first player unable to select an element of the…

This article deals with ranking methods. We study the situation where a tournament between $n$ players $P_1$, $P_2$, \ldots $P_n$ gives the ranking $P_1 \succ P_2 \succ \cdots \succ P_n$, but, if the results of $P_n$ are no longer taken…

We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games. In quantum game theory, a subset of Subtraction…

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…

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…

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 consider a game in which a blindfolded player attempts to set $n$ counters lying on the vertices of a rotating regular $n$-gon table simultaneously to $0$. When the counters count$\pmod{m}$ we simplify the argument of Bar Yehuda, Etzion,…

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.…