  For an infinite-horizon continuous-time optimal stopping problem under
non-exponential discounting, we look for an optimal equilibrium, which
generates larger values than any other equilibrium does on the entire state
space. When the discount function is log sub-additive and the state process is
one-dimensional, an optimal equilibrium is constructed in a specific form,
under appropriate regularity and integrability conditions. While there may
exist other optimal equilibria, we show that they can differ from the
constructed one in very limited ways. This leads to a sufficient condition for
the uniqueness of optimal equilibria, up to some closedness condition. To
illustrate our theoretic results, comprehensive analysis is carried out for
three specific stopping problems, concerning asset liquidation and real options
valuation. For each one of them, an optimal equilibrium is characterized
through an explicit formula.
