I'm looking through many sources, such as this one that mention algorithms, and time complexity of finding mixed strategy Nash equilibria.
But is there any algorithm for finding pure strategy Nash equilibria? This algorithm does not need to be fast (as this problem is in NP, as far as I have read).
The trivial solution would be to check every single strategy profile, but this would be time complexity $O(\prod^{N}_{i=1} n_i)$, where N is the number of players, and n is an array containing how many pure strategies each player has