  Recently, Farnik asked whether the hat guessing number $\text{HG}(G)$ of a
graph $G$ could be bounded as a function of its degeneracy $d$, and Bosek,
Dudek, Farnik, Grytczuk and Mazur showed that $\text{HG}(G)\ge 2^d$ is
possible. We show that for all $d\ge 1$ there exists a $d$-degenerate graph $G$
for which $\text{HG}(G) \ge 2^{2^{d-1}}$. We also give a new general method for
obtaining upper bounds on $\text{HG}(G)$. The question of whether
$\text{HG}(G)$ is bounded as a function of $d$ remains open.
