Stable matching problem is greedy or Dynamic?
If you consider the Gale–Shapley algorithm, it takes a greedy approach.

By the definition of Wikipedia:


  A greedy algorithm is an algorithmic paradigm that follows the problem
  solving heuristic of making the locally optimal choice at each stage
  with the hope of finding a global optimum.


The Gale-Shapley Algorithm does exactly that. At each step, the 'proposers' take a greedy decision of selecting the best partner (locally optimal choice) that was not yet proposed.