Is decision making/theory/analysis applicable to game design?
This question seems to arise out of a slight terminological confusion. Empirical studies of human decision-making in particular are not covered by decision theory. Decision theory is the mathematical study of strategies for optimal decision-making between options involving different risks or expectations of gain or loss depending on the outcome. These sometimes overlap, such as in economics, but one need not use decision theory to study decision making.

Decision theory could conceivably have some uses in game design, such as identifying dominant strategies (strategies that are always optimal, regardless of what any other player does), but decision theory takes the game rules as a given. Hence, while it can help formalize the mechanics of a set of rules once they are designed, it doesn't have a way to actually generate rules. Decision theory is not so much helpful in designing game rules as in evaluating them.

You may be interested in what's called mechanism design theory, or reverse game theory. In contrast to decision theory, mechanism design theory is designed to work 'forwards' rather than 'backwards.' Instead of taking the rules of the game (or mechanism) as a given, mechanism design theory takes the goal as a given and finds a suitable mechanism. This seems to more closely fit what the question is looking for.