  The moduli space of holomorphic maps from Riemann surfaces to the
Grassmannian is known to have two kinds of compactifications: Kontsevich's
stable map compactification and Marian-Oprea-Pandharipande's stable quotient
compactification. Over a non-singular curve, the latter moduli space is
Grothendieck's Quot scheme. In this paper, we give the notion of
`$\epsilon$-stable quotients' for a positive real number $\epsilon$, and show
that stable maps and stable quotients are related by the wall-crossing
phenomena. We will also discuss Gromov-Witten type invariants associated to
$\epsilon$-stable quotients, and investigate them under the wall-crossing.
