  Combinatorial two-player games have recently been applied to knot theory.
Examples of this include the Knotting-Unknotting Game and the Region Unknotting
Game, both of which are played on knot shadows. These are turn-based games
played by two players, where each player has a separate goal to achieve in
order to win the game. In this paper, we introduce the Linking-Unlinking Game
which is played on two-component link shadows. We then present winning
strategies for the Linking-Unlinking Game played on all shadows of
two-component rational tangle closures and played on a large family of general
two-component link shadows.
