Related papers: A New Twist on Wythoff's Game

Subtraction games are played with one or more heaps of tokens, with players taking turns removing from a single heap a number of tokens belonging to a specified subtraction set; the last player to move wins. We describe how to compute the…

We introduce a pebble game extended by backtracking options for one of the two players (called Prover) and reduce the provability of the pigeonhole principle for a generic predicate $R$ in the bounded arithmetic $T^2_2(R)$ to the existence…

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…

We consider the following combinatorial two-player game: On the random tree arising from a branching process, each round one player (Breaker) deletes an edge and by that removes the descendant and all its progeny, while the other (Maker)…

The class of Poset Take-Away games includes many interesting and difficult games. Playing on an $n$-dimensional positive quadrant (the origin being the bottom of the poset) gives rise to nim, wythoff's nim and chomp. These are impartial…

We present a novel two-player game in a chaotic dynamical system where players have opposing objectives regarding the system's behavior. The game is analyzed using a methodology from the field of chaos control known as partial control. Our…

We introduce a 2-player game played on an infinite grid, initially empty, where each player in turn chooses a vertex and colours it. The first player aims to create some pattern from a target set, while the second player aims to prevent it.…

We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…

We consider two-player stochastic games played on a finite graph for infinitely many rounds. Stochastic games generalize both Markov decision processes (MDP) by adding an adversary player, and two-player deterministic games by adding…

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…

Poset games are a class of combinatorial game that remain unsolved. Soltys and Wilson proved that computing wining strategies is in \textbf{PSPACE} and aside from special cases such as Nim and N-Free games, \textbf{P} time algorithms for…

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…

The game Arc-Kayles is played on an undirected graph with two players taking turns deleting an edge and its endpoints from the graph. We study a generalization of this game, Weighted Arc Kayles (WAK for short), played on graphs with…

Recently, Press and Dyson have proposed a new class of probabilistic and conditional strategies for the two-player iterated Prisoner's Dilemma, so-called zero-determinant strategies. A player adopting zero-determinant strategies is able to…

In this paper, we extend the Descent framework, which enables learning and planning in the context of two-player games with perfect information, to the framework of stochastic games. We propose two ways of doing this, the first way…

This paper considers the effect of riffle shuffling on decks of cards, allowing for some cards to be indistinguishable from other cards. The dual problem of dealing a game with hands, such as bridge or poker, is also considered. The…

We construct a statistical ensemble of games, where in each independent subensemble we have two players playing the same game. We derive the mean payoffs per move of the representative players of the game, and we evaluate all the…

Combinatorial games are played under two different play conventions: normal play, where the last player to move wins, and \mis play, where the last player to move loses. Combinatorial games are also classified into impartial positions and…

For a poset $P$, an Ungar move sends $P$ to $P\setminus T$, where $T$ is some subset of maximal elements of $P$. With these Ungar moves, Defant, Kravitz, and Williams define the Ungar games, where two players alternate making nontrivial…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…