Related papers: The Shortest Connection Game
The edges of a graph are assigned weights and passage times which are assumed to be positive integers. We present a parallel algorithm for finding the shortest path whose total weight is smaller than a pre-determined value. In each step the…
A subset of the vertex set of a graph is geodetically convex if it contains every vertex on any shortest path between two elements of the subset. The convex hull of a set of vertices is the smallest convex set containing the set. We study…
An alternating graph is a directed graph whose vertex set is partitioned into two classes, existential and universal. This forms the basic arena for a plethora of infinite duration two-player games where Player~$\square$ and~$\ocircle$…
The online semi-random graph process is a one-player game which starts with the empty graph on $n$ vertices. At every round, a player (called Builder) is presented with a vertex $v$ chosen uniformly at random and independently from previous…
We investigate a two player game called the $K^4$-building game: two players alternately claim edges of an infinite complete graph. Each player's aim is to claim all six edges on some vertex set of size four for themself. The first player…
We consider a variation on Maker-Breaker games on graphs or digraphs where the edges have random costs. We assume that Maker wishes to choose the edges of a spanning tree, but wishes to minimise his cost. Meanwhile Breaker wants to make…
We consider a constrained version of the shortest path problem on the complete graphs whose edges have independent random lengths and costs. We establish the asymptotic value of the minimum length as a function of the cost-budget within a…
We introduce a network design game where the objective of the players is to design the interconnections between the nodes of two different networks $G_1$ and $G_2$ in order to maximize certain local utility functions. In this setting, each…
The semi-random graph process is a single-player game that begins with an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then adaptively selects a vertex…
The Explorer-Director game, first introduced by Nedev and Muthukrishnan, can be described as a game where two players -- Explorer and Director -- determine the movement of a token on the vertices of a graph. At each time step, the Explorer…
With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…
We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary tries to set an ambush. A two players zero sum game is introduced. Players' strategies are computed as random path…
Congestion games are a classical type of games studied in game theory, in which n players choose a resource, and their individual cost increases with the number of other players choosing the same resource. In network congestion games…
Network congestion games are a convenient model for reasoning about routing problems in a network: agents have to move from a source to a target vertex while avoiding congestion, measured as a cost depending on the number of players using…
We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the…
Shortest-path games are two-player zero-sum games played on a graph equipped with integer weights. One player, that we call Min, wants to reach a target set of states while minimising the total weight, and the other one has an antagonistic…
In this paper we study the (a : b) Maker-Breaker Connectivity game, played on the edge-set of the complete graph on n vertices. We determine the winner for almost all values of a and b.
Edge and vertex connectivity are fundamental concepts in graph theory. While they have been thoroughly studied in the case of undirected graphs, surprisingly not much has been investigated for directed graphs. In this paper we study…
A good computer network is hard to disrupt. It is desired that the computer communication network remains connected even when some of the links or nodes fail. Since the communication links are expensive, one wants to achieve these goals…
We consider zero-sum games in which players move between adjacent states, where in each pair of adjacent states one state dominates the other. The states in our game can represent positional advantages in physical conflict such as high…