  Several problems in planning and reactive synthesis can be reduced to the
analysis of two-player quantitative graph games. {\em Optimization} is one form
of analysis. We argue that in many cases it may be better to replace the
optimization problem with the {\em satisficing problem}, where instead of
searching for optimal solutions, the goal is to search for solutions that
adhere to a given threshold bound.
  This work defines and investigates the satisficing problem on a two-player
graph game with the discounted-sum cost model. We show that while the
satisficing problem can be solved using numerical methods just like the
optimization problem, this approach does not render compelling benefits over
optimization. When the discount factor is, however, an integer, we present
another approach to satisficing, which is purely based on automata methods. We
show that this approach is algorithmically more performant -- both
theoretically and empirically -- and demonstrates the broader applicability of
satisficing overoptimization.
