Sorry I do not know much about game theory, but if you have some data with features and a label (indicating a type of game theory) yes you can probably use some supervised learning algorithms.
I work mostly with scikit-learn python package that offers some of main algorithms (in annexed figure). What kind of help do you need?
I don't know so much about supervised learning methods, however, the first step to use the game theory is to identify your players (players of the game) and scenarios of each player.
You can check our book chapter (first part), in which we define what is game theory.