Related papers: Computational Properties of Slime Trail
We introduce a new positional game called `Toucher-Isolator', which is a quantitative version of a Maker-Breaker type game. The playing board is the set of edges of a given graph G, and the two players, Toucher and Isolator, claim edges…
A team of $r$ {\it revolutionaries} and a team of $s$ {\it spies} play a game on a graph $G$. Initially, revolutionaries and then spies take positions at vertices. In each subsequent round, each revolutionary may move to an adjacent vertex…
A natural partial ordering exists on the set of all weighted games and, more broadly, on all linear games. We describe several properties of the partially ordered sets formed by these games and utilize this perspective to enumerate proper…
We use matrix iteration theory to characterize acceleration in smooth games. We define the spectral shape of a family of games as the set containing all eigenvalues of the Jacobians of standard gradient dynamics in the family. Shapes…
The Honey-Bee game is a two-player board game that is played on a connected hexagonal colored grid or (in a generalized setting) on a connected graph with colored nodes. In a single move, a player calls a color and thereby conquers all the…
We study the class of potential games that are also graphical games with respect to a given graph $G$ of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of…
The pressing game on black-and-white graphs is the following: Given a graph $G(V,E)$ with its vertices colored with black and white, any black vertex $v$ can be pressed, which has the following effect: (a) all neighbors of $v$ change color,…
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…
In this paper we analyse two-player games by their response graphs. The response graph has nodes which are strategy profiles, with an arc between profiles if they differ in the strategy of a single player, with the direction of the arc…
We study a simple adaptive model in the framework of an N -player normal form game. The model consists of a repeated game where the players only know their own action space and their own payoff scored at each stage, not those of the other…
A new mathematical model for evolutionary games on graphs is proposed to extend the classical replicator equation to finite populations of players organized on a network with generic topology. Classical results from game theory,…
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…
Fay, Hurlbert and Tennant recently introduced a one-player game on a finite connected graph $G$, which they called cup stacking. Stacks of cups are placed at the vertices of $G$, and are transferred between vertices via stacking moves,…
We study a game where two players take turns selecting points of a convex geometry until the convex closure of the jointly selected points contains all the points of a given winning set. The winner of the game is the last player able to…
We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing…
We study a patrolling game played on a network $Q$, considered as a metric space. The Attacker chooses a point of $Q$ (not necessarily a node) to attack during a chosen time interval of fixed duration. The Patroller chooses a unit speed…
We introduce the game INFLUENCE, a scoring combinatorial game, played on a directed graph where each vertex is either colored black or white. The two players, Black and White play alternately by taking a vertex of their color and all its…
In this work we propose a game theoretic model for document clustering. Each document to be clustered is represented as a player and each cluster as a strategy. The players receive a reward interacting with other players that they try to…
Using a particle model of slime mould we demonstrate scoping experiments which explore how path planning may be performed by morphological adaptation. We initially demonstrate simple path planning by a shrinking blob of virtual plasmodium…
Prefetching constitutes a valuable tool toward efficient Web surfing. As a result, estimating the amount of resources that need to be preloaded during a surfer's browsing becomes an important task. In this regard, prefetching can be modeled…