A cooperative game often arises from domination problem on graphs and the core in a cooperative game could be the optimal solution of a linear programming of a given game. In this paper, we define a {k}-fractional domination game which is a specific type of fractional domination games and find the core of a {k}-fractional domination game. Moreover, we may investigate the balancedness of a {k}-fractional domination game using a concept of a linear programming and duality. We also conjecture the concavity for {k}-fractional dominations game which is important problem to find the elements of the core.