/sci/ - Science & Math

Nash's theorem for (finite) general-sum games states that each such game admits a Nash equilibrium. The proof I'm familiar with goes through Brouwer's FPT, which of course is non-constructive.

Given an arbitrary game, can one prove the existence of a Nash equilibrium constructively? I'm asking because there are bi-matrix game solvers abundant online, so it seems like there's a feasible algorithm for the problem; I know that for the special case of zero games, solving the game simply reduces to LP, which of course is computationally solvable. But is the problem of finding a Nash equilibrium in a general-sum [math]n[/math] player game even decidable?