2. Let $k$ be a constant. If for all $x, y \in(0,1)$, we have
$$
x^{k}+y^{k}-x^{k} y^{k} \leqslant \frac{1}{x^{k}}+\frac{1}{y^{k}}-\frac{1}{x^{k} y^{k}},
$$

then the range of the real number $k$ is $\qquad$ .
2. $(-\infty, 0]$.

Notice that
$$
\begin{array}{l}
x^{k}+y^{k}-x^{k} y^{k} \leqslant \frac{1}{x^{k}}+\frac{1}{y^{k}}-\frac{1}{x^{k} y^{k}} \\
\Leftrightarrow\left(1-x^{k}\right)\left(1-y^{k}\right) \geqslant\left(1-\frac{1}{x^{k}}\right)\left(1-\frac{1}{y^{k}}\right) \\
\Leftrightarrow x^{k} y^{k} \geqslant 1 \Leftrightarrow k \leqslant 0 .
\end{array}
$$