Consider a 2 player game with payoff matrices A and B in which each of the players has n strategies (i.e.so that each of A and B are n * n matrices). Assume the entries of A and B are distributed uniformly in the range [0, 1] and are sampled independently of the others.

Show that the probability that the game has a dominated strategy equilibrium is exponentially small in n

(A dominated strategy equilibrium is an equilibrium that can be found by eliminating dominated strategies).