The domination game is played on a graph G by Dominator and Staller. The two players are taking turns choosing a vertex from G such that at least one previously undominated vertex becomes dominated; the game ends when no move is possible. The game is called D-game when Dominator starts it, and S-game otherwise. Dominator wants to finish the game as fast as possible, while Staller wants to prolo...

In this paper we present an overview of a variety of efforts to attain good performance of Game AI for Domination games. These are a very popular kind of game sub-genre in which teams compete for control of locations. Due to the rules of the games, good performance is mostly dependant on overall strategy rather than the skill of individual team members.

A two person (or bimatrix) game is a pair of m x n matrices A. B, with integer entries. This game is played between two players A and B. Player A chooses a row t. player B simultaneously chooses a column j. As a result. A receives a,, (dollars, say), and B receives b,,. An easy way to simplify a bimatrix game is to eliminate from both A and B any strategy (row or column) that is dominated by an...

We present an algorithm which determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player. Our algorithm performs a recursive descent search of the game-tree, combining fixed and dynamic game-state virtual connection composition rules with some new Hex game-state reduction results based on move domination. The algorithm is powerful enough...

We present an algorithm which determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player. Our algorithm performs a recursive descent search of the game-tree, combining fixed and dynamic game-state virtual connection composition rules with some new Hex game-state reduction results based on move domination. The algorithm is powerful enough...

We study Maker--Breaker total domination game played by two players, Dominator and Staller, on the connected cubic graphs. Staller (playing role of Maker) wins if she manages to claim an open neighbourhood a vertex. otherwise (i.e.\ he can dominating set graph). For certain graphs $n\geq 6$ vertices, we give characterization those which are Dominator's win Staller's win.