Is decision making/theory/analysis applicable to game design? I've done research over the last year in game design by reading some of the most well-known books in the field. Making interesting decisions is one of the fundamental elements of fun in games. I'm also learning( still a novice ) about cognition through two classes I'm taking the semester, Psychology of HCI and Human Factors Engineering. 

It seems that what is said about decision making in cognitive psychology could also apply to the decisions we make in games. There's definitely choice and uncertainty while making these choices in games. 

It seems one of the hardest parts of game design is coming up with game mechanics that cause the player to make interesting decisions based on these game mechanics. 

Could studying decision making/theory/analysis possibly help with this process of creating good game mechanics where interesting decisions emerge from the player analyzing and making decisions based on these mechanics?

It seems obvious that this would be the case, but here recently I talked to someone in the psychology department who has a lot of experience in the subject of decision making who told me that it's not the same thing. They said decision making in the cognitive psychology realm isn't the same as decision making in games. They said you make weighted choices based on your options while playing games, which seems the same to me. But I'm still a novice in cognitive psychology so I feel I must trust the expert. 

This is my attempt to get a second opinion.
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.