We shall present several game theoretic problems on graphs which stem
from classical combinatorial problems. Games on graphs are usually
(NP/PSPACE/EXPTIME) hard, as the graph structure gives rise to high
complexity. To tackle these problems we may employ methods used for
tackling classical problems, e.g., restricting the problem to a graph
class or to analyze the problem using parameterized complexity. Our
focus will be on Online Ramsey theory, Eternal domination, and group
identification problem.