704. State-Based Actions

704.1. State-based actions are game actions that happen automatically whenever certain conditions (listed below) are met. State-based actions don't use the stack.
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704.2. State-based actions are checked throughout the game and are not controlled by any player.
704.3. Whenever a player would get priority (see rule 116, "Timing and Priority"), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event. If any state-based actions are performed as a result of a check, the check is repeated; otherwise all triggered abilities that are waiting to be put on the stack are put on the stack, then the check is repeated. Once no more state-based actions have been performed as the result of a check and no triggered abilities are waiting to be put on the stack, the appropriate player gets priority. This process also occurs during the cleanup step (see rule 514), except that if no state-based actions are performed as the result of the step's first check and no triggered abilities are waiting to be put on the stack, then no player gets priority and the step ends.
704.4. Unlike triggered abilities, state-based actions pay no attention to what happens during the resolution of a spell or ability.
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704.5b If a player attempted to draw a card from a library with no cards in it since the last time state-based actions were checked, he or she loses the game.

Bolding is my own, should sum things up pretty well :).  All players will lose the game at the same time.  As a side note, if it's a two player game, both players will lose.  If it's a two player game and Player A controls Abyssal Persecutor, Abyssal Persecutor will prevent Player B from losing and be removed from the game when Player A loses.  This leaves Player B as the only player left so they Win!  Here's to Comp Rule to back it up:

704.3. ..... If any state-based actions are performed as a result of a check, the check is repeated;
104.2a A player still in the game wins the game if all of that player's opponents have left the game. This happens immediately and overrides all effects that would prevent that player from winning the game.
104.5. If a player loses the game, he or she leaves the game. If the game is a draw for a player, he or she leaves the game. The multiplayer rules handle what happens when a player leaves the game; see rule 800.4.
800.4a When a player leaves the game, all objects (see rule 109) owned by that player leave the game, any effects which give that player control of any objects or players end, and all spells and abilities controlled by that player on the stack cease to exist. Then, if there are any objects still controlled by that player, those objects are exiled. This is not a state-based action. It happens as soon as the player leaves the game. If the player who left the game had priority at the time he or she left, priority passes to the next player in turn order who's still in the game.


[Edited by Squillis on 7/Jun/12 at 3:55PM]