On a game of Borel

A two-person game with pure strategies of players
\begin{gather*} X=(x_1,x_2,x_3),\quad x_i\ge0,\quad x_1+x_2+x_3=1; \\ Y=(y_1,y_2,y_3),\quad y_i\ge0,\quad y_1+y_2+y_3=1, \end{gather*}
and the payoff $H(X,Y)=\operatorname{sign}(y_1-x_1)(y_2-x_2)(y_3-x_3)$ is studied. A class of solutions of this game is given.