Nash equilibrium in Python

Raymond Hettinger wrote a recipe for solving zero-sum payoff matrices. It should serve your purposes alright.

As for a more general library for solving game theory, there's nothing specifically designed for that. But, like you said, scipy can tackle optimization problems like this. You might be able to do something with GarlicSim, which claims to be for "any kind of simulation: Physics, game theory..." but I've never used it before so I can't recommend it.

There is Gambit, which is a little difficult to set up, but has a python API.