Communication complexity of approximate Nash equilibria

For a constant ε, we prove a poly(N) lower bound on the (randomized) communication complexity of ε-Nash equilibrium in two-player NxN games. For n-player binary-action games we prove an exp(n) lower bound for the (randomized) communication complexity of (ε,ε)-weak approximate Nash equilibrium, which is a profile of mixed actions such that at least (1-ε)-fraction of the players are ε-best replying.