  We present a generalization of the marriage problem underlying Hall's famous
Marriage Theorem to what we call the Symmetric Marriage Problem, a problem that
can be thought of as a special case of Maximal Weighted Bipartite Matching. We
show that there is a solution to the Symmetric Marriage Problem if and only if
a variation on Hall's Condition holds on each of the bipartitions. We prove
both finite and infinite versions of this result and provide applications. We
also introduce a non-bipartite version of the problem and show that a
generalization of Tutte's Theorem applies.
