Related papers: Node-Kayles on Trees
We consider a generalization of the classical game of $NIM$ called hypergraph $NIM$. Given a hypergraph $\cH$ on the ground set $V = \{1, \ldots, n\}$ of $n$ piles of stones, two players alternate in choosing a hyperedge $H \in \cH$ and…
Rosenthal (1973) introduced the class of congestion games and proved that they always possess a Nash equilibrium in pure strategies. Fotakis et al. (2005) introduce the notion of a greedy strategy tuple, where players sequentially and…
Traditionally social sciences are interested in structuring people in multiple groups based on their individual preferences. This pa- per suggests an approach to this problem in the framework of a non- cooperative game theory. Definition of…
We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these \emph{lattice games} can be made particularly efficient for octal games, which we generalize to…
Starting with a graph, two players take turns in either deleting an edge or deleting a vertex and all incident edges. The player removing the last vertex wins. We review the known results for this game and extend the computation of…
A sequence $S$ of vertices of a graph $G$ is called a dominating sequence of $G$ if $(i)$ each vertex $v$ of $S$ dominates a vertex of $G$ that was not dominated by any of the vertices preceding vertex $v$ in $S$, and $(ii)$ every vertex of…
Every weighted tree corresponds naturally to a cooperative game that we call a "tree game"; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the…
Subtraction games is a class of combinatorial games. It was solved since the Sprague-Grundy Theory was put forward. This paper described a new algorithm for subtraction games. The new algorithm can find win or lost positions in subtraction…
Coalition formation over graphs is a well studied class of games whose players are vertices and feasible coalitions must be connected subgraphs. In this setting, the existence and computation of equilibria, under various notions of…
We introduce a class of cooperative games induced by weighted directed graphs. Specifically, the coalitional value combines an internal interaction term given by the induced subgraph game with an external component based on minimal incoming…
The arboricity of a graph is the minimum number of forests required to cover all its edges. In this paper, we examine arboricity from a game-theoretic perspective and investigate cost-sharing in the minimum forest cover problem. We…
We examine the structure of the additive period of the Sprague-Grundy function of Nim-like games, among them Wythoff's Game, and deduce a bound for the length of the period and preperiod.
The core of a game $v$ on $N$, which is the set of additive games $\phi$ dominating $v$ such that $\phi(N)=v(N)$, is a central notion in cooperative game theory, decision making and in combinatorics, where it is related to submodular…
Berlekamp proposed a class of impartial combinatorial games based on the moves of chess pieces on rectangular boards. We generalize impartial chess games by playing them on Young diagrams and obtain results about winning and losing…
The traditional mathematical model for an impartial combinatorial game is defined recursively as a set of the options of the game, where the options are games themselves. We propose a model called gamegraph, together with its generalization…
The game of Nim as played on graphs was introduced in Nim on Graphs I and extended in Nim on Graphs II by Masahiko Fukuyama. His papers detail the calculation of Grundy numbers for graphs under specific circumstances. We extend these…
The Stackelberg Minimum Spanning Tree Game is a two-level combinatorial pricing problem played on a graph representing a network. Its edges are colored either red or blue, and the red edges have a given fixed cost, representing the…
We study coalition structure formation with intra and inter-coalition externalities in the introduced family of nested non-cooperative simultaneous finite games. A non-cooperative game embeds a coalition structure formation mechanism, and…
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…
We consider a generalization of the classical game of $NIM$ called hypergraph $NIM$. Given a hypergraph $\cH$ on the ground set $V = \{1, \ldots, n\}$ of $n$ piles of stones, two players alternate in choosing a hyperedge $H \in \cH$ and…