Solution
= Solution
The <matrix> is antisymmetric, so the value is zero. For a common candidate $p=(a,b,c,d)^T$, the column-player inequalities are $Ap\le0$:
$$
b-c\le0,\qquad-a+c+2d\le0,\qquad a-b+d\le0,\qquad-2b-c\le0.
$$
The first three imply $a+d\le b\le c\le a-2d$, hence $d=0$ and $a=b=c$. Normalization gives
$$
p=q=(1/3,1/3,1/3,0)^T.
$$
Indeed $Ap=(0,0,0,-1)^T/3\le0$, and antisymmetry gives the corresponding row inequalities.