Related papers: Necklace Games
In this article we compute analytically the number of Nash Equilibria (NE) for a two-choice game played on a (circular) ladder graph with $2n$ players. We consider a set of games with generic payoff parameters, with the only requirement…
Let A be a finite subset of the naturals and let n be a natural. Let NIM(A;n) be the two player game in which players alternate removing $a\in A$ stones from a pile with $n$ stones; the first player who cannot move loses. This game has been…
Fix a finite alphabet. A necklace is a circular word. For positive integers $n$ and~$k$, a necklace is $(n,k)$-perfect if all words of length $n$ occur $k$ times but at positions with different congruence modulo $k$, for any convention of…
Subtraction games are a class of impartial combinatorial games whose positions correspond to nonnegative integers and whose moves correspond to subtracting one of a fixed set of numbers from the current position. Though they are easy to…
The rank of a bimatrix game (A,B) is defined as rank(A+B). Computing a Nash equilibrium (NE) of a rank-$0$, i.e., zero-sum game is equivalent to linear programming (von Neumann'28, Dantzig'51). In 2005, Kannan and Theobald gave an FPTAS for…
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…
We propose and analyse a 2-parameter family of 2-player games on two heaps of tokens, and present a strategy based on a class of sequences. The strategy looks easy, but is actually hard. A class of exotic numeration systems is then used,…
The class of weakly acyclic games, which includes potential games and dominance-solvable games, captures many practical application domains. In a weakly acyclic game, from any starting state, there is a sequence of better-response moves…
We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete
Infinitely repeated games support equilibrium concepts beyond those present in one-shot games (e.g., cooperation in the prisoner's dilemma). Nonetheless, repeated games fail to capture our real-world intuition for settings with many…
Distance games are games played on graphs in which the players alternately colour vertices, and which vertices can be coloured only depends on the distance to previously coloured vertices. The polynomial profile encodes the number of…
Consider a very simple class of (finite) games: after an initial move by nature, each player makes one move. Moreover, the players have common interests: at each node, all the players get the same payoff. We show that the problem of…
Motivated by the sequence form formulation of Koller et al. (GEB'96), this paper defines {\em bilinear games}, and proposes efficient algorithms for its rank based subclasses. Bilinear games are two-player non-cooperative single-shot games…
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…
Without further ado, we present the P_3-game. The P_3-game is decidable for elementary classes of graphs such as paths and cycles. From an algorithmic point of view, the connected P_3-game is fascinating. We show that the connected P_3-game…
Neighborhood Lights Out is a game played on graphs. Begin with a graph and a vertex labeling of the graph from the set $\{0,1,2,\dots, \ell-1\}$ for $\ell \in \mathbb{N}$. The game is played by toggling vertices: when a vertex is toggled,…
We study the complexity of solving two-player infinite duration games played on a fixed finite graph, where the control of a node is not predetermined but rather assigned randomly. In classic random-turn games, control of each node is…
Fibonacci nim is a popular impartial combinatorial game, usually played with a single pile of stones. The game is appealing due to its surprising connections with the Fibonacci numbers and the Zeckendorf representation. In this article, we…
In a monotonic sequence game, two players alternately choose elements of a sequence from some fixed ordered set. The game ends when the resulting sequence contains either an ascending subsequence of length a or a descending one of length d.…
Games such as go, chess and checkers have multiple equivalent game states, i.e. multiple board positions where symmetrical and opposite moves should be made. These equivalences are not exploited by current state of the art neural agents…