Related papers: Delete Nim
We investigate zero-sum turn-based two-player stochastic games in which the objective of one player is to maximize the amount of rewards obtained during a play, while the other aims at minimizing it. We focus on games in which the minimizer…
A general model for zero-sum stochastic games with asymmetric information is considered. In this model, each player's information at each time can be divided into a common information part and a private information part. Under certain…
In this paper we study a variant of the Nuel game (a generalization of the duel) which is played in turns by $N$ players. In each turn a single player must fire at one of the other players and has a certain probability of hitting and…
This paper consider the possibility of using some quantum tools in decision making strategies. In particular, we consider here a dynamical open quantum system helping two players, $\G_1$ and $\G_2$, to take their decisions in a specific…
In the gift exchange game there are n players and n wrapped gifts. When a player's number is called, that person can either choose one of the remaining wrapped gifts, or can "steal" a gift from someone who has already unwrapped it, subject…
We consider a game with two piles, in which two players take turn to add $a$ or $b$ chips ($a$, $b$ are not necessarily positive) randomly and independently to their respective piles. The player who collects $n$ chips first wins the game.…
This thesis will be discussing scoring play combinatorial games and looking at the general structure of these games under different operators. I will also be looking at the Sprague-Grundy values for scoring play impartial games, and…
Motivated by the burning and cooling processes, the burning game is introduced. The game is played on a graph $G$ by the two players (Burner and Staller) that take turns selecting vertices of $G$ to burn; as in the burning process, burning…
Dominance is a fundamental concept in game theory. In normal-form games dominated strategies can be identified in polynomial time. As a consequence, iterative removal of dominated strategies can be performed efficiently as a preprocessing…
We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an…
In the game of $n-Sim$, two players take it in turn to claim unclaimed edges from a complete graph on $n$ vertices, with the first person to create a triangle in his own edges being the loser. We present some strategy-stealing arguments…
The isolation game is played on a graph $G$ by two players who take turns playing a vertex such that if $X$ is the set of already played vertices, then a vertex can be selected only if it dominates a vertex from a nontrivial component of $G…
We revisit the problem of solving two-player zero-sum games in the decentralized setting. We propose a simple algorithmic framework that simultaneously achieves the best rates for honest regret as well as adversarial regret, and in addition…
The balance game is played on a graph $G$ by two players, Admirable (A) and Impish (I), who take turns selecting unlabeled vertices of $G$. Admirable labels the selected vertices by $0$ and Impish by $1$, and the resulting label on any edge…
Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of…
Computing Nash equilibrium (NE) of multi-player games has witnessed renewed interest due to recent advances in generative adversarial networks. However, computing equilibrium efficiently is challenging. To this end, we introduce the…
A move in the game of nim consists of taking any positive number of tokens from a single pile. Suppose we add the class of moves of taking a nonnegative number of tokens jointly from all the piles. We give a complete answer to the question…
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…
We study 2-player impartial games, so called \emph{invariant subtraction games}, of the type, given a set of allowed moves the players take turn in moving one single piece on a large Chess board towards the position $\boldsymbol 0$. Here,…
Two players alternate moves in the following impartial combinatorial game: Given a finitely generated abelian group $A$, a move consists of picking some nonzero element $a \in A$. The game then continues with the quotient group $A/ \langle…