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I'm a Java programmer interested to learn games on Java, recently I looked on a book on Operations Research written by Wayne L.Winston. There is a topic on Game Theory.
It's truly mathematical. I'm just an app developer, but would that book be helpful to start a game career?
The game in game theory and game development are not talking about the same kind of games. Game theory is mainly used in economics and political science. Sounds like the book you were reading was about business strategy?
I would say it's more accurate to say that game theory can be applied to computer science and the development of logical theories related to high level algorithms. But studying game theory will not necessarily help you become a better game developer.
Most of the games in game theory wouldn't make very good video games. For example, one game goes something like this:
There are people bidding on $100. The rules are if you win you pay what you bid and get the $100. If you're in second you also pay what you bid but you don't get anything. A pretty boring game and if the bids go over $100 both people lose.
The kind of things you'd learn in game theory would probably apply more to thinking about how a player might approach your game rather than help development. Since I feel like the other posts have already established that it wouldn't really be beneficial, altough its pretty interesting if you're into that kind of thing, I'll talk about maths that might be helpful.
Linear algebra is a must, mostly because it's used in a lot of other branches of math, including game theory. It's the kind of math I've run into the most when developing games. I imagine if one got into engine development this kind of math would be even more relavant. It's also more useful in 3D games as opposed to 2D.
Combinatorial maths could be helpful. Especially for probability. Also Combinatorial game theory is about games but exclusively turn based and generally the games are simple.
Discrete probability is also useful. I haven't really seen too much continuous stuff but discrete things come up quite often and might actually cut back on testing time. Basically any time you use random numbers you'd use probability. Sometimes it's pretty basic but who knows, sometimes probability problems look a lot less involved than they actually are.
And I imagine if you were to develop a physics engine Calculus would be used but I don't know anything about engine development.
There is a relationship, as game theory is also known as "interactive decision theory" (Wikipedia), but it's an extremely complex subject and you would probably be better off starting down a more traditional path.
Basically, yes it would be helpful, but there are arguably "better" ways to start game development, like studying the fundamentals of computer science.
