If you don't need the problem to break pages, it seems pretty simple to hack something together using
\fbox and a hanging indent:
Input: A SAT formula $\phi(x_1,\dots,x_n)$
Question: Two players, the Prover and the Skeptic, take turns setting the $x_i$.
The Prover sets $x_1$, then the Skeptic sets $x_2$, and so on.
After all the variables are set, the Prover wins if $\phi$ is true,
and the Skeptic wins if $\phi$ is false.
Does the Prover have a winning strategy?
If problems must break pages, look into using