Is Game Theory a Self-Contained Subject?

[bballwaterboy]

I'm very intrigued by game theory after watching a little puzzle on YouTube that was part of a game show.

The solution or best strategy turned out to be solved through game theory.

Anyhow, I further checked out an introduction to game theory online and there didn't seem to be any "regular' math that I had ever had before. There were just these "pay-off" cubes with numbers in them.

For someone who has only had math through Calculus, would it be possible to learn game-theory on my own in a book or some other format without having had higher math? Or do you need some other kind of math mid-way through the subject? I find it to be the most fun math-like topic I've seen so far, but we don't have anything like this at my community college.

If it is a self-contained math topic, then I'd love to learn about it over the upcoming summer (I'll be transferring to a regular university next academic year). And if anyone has any book recommendations for good intro to game theory, I'd definitely take a look.

Appreciate it guys!

 

[HallsofIvy]

For the very simple games that you are referring to, zero sum, two person, games with a finite number of strategies, you don't need more than basic algebra and some probability theory. However, non-zero sum games, games with a number of people, allowing cooperation, infinite strategies or infinite variations of strategies, will require Calculus, Linear Programming, etc.

 

[FactChecker]

Von Neumann founded the field of game theory and wrote a heavily mathematical book "Theory of Games and Economic Behavior". It will really hurt your head. I see that there is a book "The Complete Idiot's Guide to Game Theory" which has good reviews on Amazon. That is probably more my style and I am tempted to get it. (I am a fan of "Idiot's Guide" books) But I have not seen it yet.

 

[bballwaterboy]

For the very simple games that you are referring to, zero sum, two person, games with a finite number of strategies, you don't need more than basic algebra and some probability theory. However, non-zero sum games, games with a number of people, allowing cooperation, infinite strategies or infinite variations of strategies, will require Calculus, Linear Programming, etc.

Thanks, Halls!

Von Neumann founded the field of game theory and wrote a heavily mathematical book "Theory of Games and Economic Behavior". It will really hurt your head. I see that there is a book "The Complete Idiot's Guide to Game Theory" which has good reviews on Amazon. That is probably more my style and I am tempted to get it. (I am a fan of "Idiot's Guide" books) But I have not seen it yet.

I'll take a look.

Thanks. And if anyone else has any recommendations, then I wouldn't mind taking a look as well. I have a long summer ahead in May and plan to do lots of reading...in every subject! So much stuff I want to learn this summer!

 

[chiro]

I'd actually recommend you be able to study graduate statistical inference.

If you understand how to construct the best estimators that use information (like in a sample) and also optimize (in a minimization sense) the loss function then you will understand quite a lot about game theory.

Game theory in essence tries to make the best use of information so that it can understand not only the game evolves - but also how to best use that information to "win". This is what statistical inference looks at - you basically have uncertainty and some information and in combination with assumptions you use that to construct an estimator which helps construct a set of decision functions which are used to make decisions regarding the next outcome in the game.

I have to warn you though that you will need a good intuitive understanding (as opposed to just a mathematical understanding) of statistics and probability to get what is actually going on in the theorems, derivations, proofs and mathematical ideas.

But if you don't want to do that you should probably just remember that you are trying to make the best use of information and find mathematically consistent ways of doing so - that is what game theory and statistical inference is all about.