  We study an infinite-horizon discrete-time optimal stopping problem under
non-exponential discounting. A new method, which we call the iterative
approach, is developed to find subgame perfect Nash equilibria. When the
discount function induces decreasing impatience, we establish the existence of
an equilibrium through fixed-point iterations. Moreover, we show that there
exists a unique optimal equilibrium, which generates larger value than any
other equilibrium does at all times. To the best of our knowledge, this is the
first time a dominating subgame perfect Nash equilibrium is shown to exist in
the literature of time-inconsistency.
