What happens if neither player decides to do anything?
The most likely outcome is that one player loses when he has no more cards to draw:


  104.3c If a player is required to draw more cards than are left in his or her library, he or she draws the remaining cards, and then loses the game the next time a player would receive priority. 


Other possible outcome is a draw during a tournament game with time limit, though a player will likely run out of cards before they reach the limit.