Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers" (per Wikipedia). By this definition, as I understand it, any game studied requires at least 2 participants.
But say we want to study strategies for what the layman might call a single-player game, with imperfect or secret information, such as a solitaire card game. Under what field or name would such a thing be studied?
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Generally, the other opponent in this case is "nature" or some other system that does not have a capability to choose responses to your actions. This falls under the domain of decision analysis. Here's a paper that explores this idea.
Economists call the one-player analogue of game theory decision theory.
Indeed, before game theory was a standard part of the economist's toolkit, it was sometimes called "multiperson decision theory".