What kind of mathematics is required by game theory?

Question

I want to learn about game theory, but I do not know if I have the necessary background to do so.

What kind of mathematics does game theory involve the most? What are some of the things that an undergrad in mathematics might not have seen which arises in game theory?

Answer 1

Perhaps the main thing that you will come up with and with which you will not be familiar as an undergraduate student are fixed point theorems (functional analysis) and linear or/and dynamic programming.

Generally, for an undergraduate course in game theory you will mostly need to be familiar with the following:

1. solving quadratic equations, maximizing/minimizing functions (mostly polynomial functions),
2. certainly some combinatorics (mainly in cooperative game theory) and some basics in probability and - depending on the professor -
3. the basics of linear programming.
4. additionally basic concepts from linear algebra (calculating the determinant of a matrix etc.) can be also required.

In sum, if you are in a "good shape" as far as the basics of linear algebra, probability and calculus are concerned then you will have no problem. But do not think that it stops here in game theory...