Let me first tell you that there are three types of economic theory:
- price theory
- general equilibrium
- game theory
Nowadays, the last type of theory is by far the most popular, but maybe you need some familiarity with the other two to appreciate game theory as an economist does. I guess you could say the mathematics is very easy judged from what mathematicians are used to. What is difficult is the economic interpretation. For that you need a bit economic intuition and a bit of culture about classic economic models.
My recommendations for a mathematically mature neophyte would be:
- george stigler's price theory for the first
- debreu's classic for general equilibrium; there is also a book by JWS Cassels
- Fudenberg & Tirole or Vega Redondo for game theory