This is backwards. Decision theory, which is the foundation of inference in statistics today (Bayesian, minimax, etc. are all special cases of it) is formulated as a one player game. Certain things mesh nicely when you realize this. For example, we know that there is a Nash equilibrium for large classes of games if we allow random strategies. Likewise, for decision theory with nonconvex loss functions, optimal procedures are almost always random.

But: game theory of two or more players is qualitatively different. For a one player game, we speak of optimal strategies. For multiplayer, noncooperative games, Nash equilibria take what would seem to be the obvious generalization of that and twist it in a whole new direction.

"Decision theory is 1-player game theory" -- I think I saw this on LessWrong, once, but I can't find it now.

Theory of games is VERY old, predating most other groundbreaking work (Nash, Shapley, Myerson, etc.)