If you don't need the problem to break pages, it seems pretty simple to hack something together using \fbox
and a hanging indent:
\documentclass{article}
\usepackage{environ}
\NewEnviron{problem}[1]{%
\begin{center}\fbox{\parbox{3in}{%
{\centering\scshape #1\par}%
\parskip=1ex
\everypar{\hangindent=1em}%
\BODY
}}\end{center}}
\begin{document}
\begin{problem}{Two-Player SAT}
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?
\end{problem}
\end{document}
-

If problems must break pages, look into using mdframed
.