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.