My question is about Magic The Gathering. What happens if both players perpetually decide to do nothing in a turn, except draw and then discard to 7. What happens then?
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.