  We consider a partially asymmetric multi-players zero-sum game with two
strategic variables. All but one players have the same payoff functions, and
one player (Player $n$) does not. Two strategic variables are $t_i$'s and
$s_i$'s for each player $i$. Mainly we will show the following results. 1) The
equilibrium when all players choose $t_i$'s is equivalent to the equilibrium
when all but one players choose $t_i$'s and Player $n$ chooses $s_n$ as their
strategic variables. 2) The equilibrium when all players choose $s_i$'s is
equivalent to the equilibrium when all but one players choose $s_i$'s and
Player $n$ chooses $t_n$ as their strategic variables. The equilibrium when all
players choose $t_i$'s and the equilibrium when all players choose $s_i$'s are
not equivalent although they are equivalent in a symmetric game in which all
players have the same payoff functions.
