  In this note we provide a new proof for the results of Lipton et al. on the
existence of an approximate Nash equilibrium with logarithmic support size.
Besides its simplicity, the new proof leads to the following contributions:
  1. For n-player games, we improve the bound on the size of the support of an
approximate Nash equilibrium.
  2. We generalize the result of Daskalakis and Papadimitriou on small
probability games from the two-player case to the general n-player case.
  3. We provide a logarithmic bound on the size of the support of an
approximate Nash equilibrium in the case of graphical games.
