  We consider the relation between Sion's minimax theorem for a continuous
function and a Nash equilibrium in an asymmetric multi-players zero-sum game in
which only one player is different from other players, and the game is
symmetric for the other players. Then,
  1. The existence of a Nash equilibrium, which is symmetric for players other
than one player, implies Sion's minimax theorem for pairs of this player and
one of other players with symmetry for the other players.
  2. Sion's minimax theorem for pairs of one player and one of other players
with symmetry for the other players implies the existence of a Nash equilibrium
which is symmetric for the other players.
  Thus, they are equivalent.
