>>11683668Anon for game theory you would need to have a competing party. A game is formally defined as having N players, each with a choice of strategy S, and each Strategy and strategy combination (with that of the other players) leading to a particular pay off for everyone. The fun comes when you analyse how players choose their courses of action according to the payoffs.
I'm not aware if puzzle solving like what you're suggesting has been/can be formulated and analysed game theoretically, I haven't really dived that deep into GT yet.