  We prove the existence of approximate correlated equilibrium of support size
polylogarithmic in the number of players and the number of actions per player.
In particular, using the probabilistic method, we show that there exists a
multiset of polylogarithmic size such that the uniform distribution over this
multiset forms an approximate correlated equilibrium. Along similar lines, we
establish the existence of approximate coarse correlated equilibrium with
logarithmic support.
  We complement these results by considering the computational complexity of
determining small-support approximate equilibria. We show that random sampling
can be used to efficiently determine an approximate coarse correlated
equilibrium with logarithmic support. But, such a tight result does not hold
for correlated equilibrium, i.e., sampling might generate an approximate
correlated equilibrium of support size \Omega(m) where m is the number of
actions per player. Finally, we show that finding an exact correlated
equilibrium with smallest possible support is NP-hard under Cook reductions,
even in the case of two-player zero-sum games.
