Crafty Cutpurse

If a token would be created tapped and attacking, but the token’s controller isn’t an attacking player, that token is created tapped but not attacking. If a token would be created blocking a creature, but the token’s controller isn’t a defending player, that token is created but isn’t blocking.

On the other hand, if the effect that creates the token grants a triggered ability to the token, the player who controls the token at the time the ability triggers will be the player who controls that ability. For example, if your opponent activates the second ability of Jace, Cunning Castaway, the token has the ability. If the ability triggers, you’ll control it, so you’ll have to sacrifice the token.

The above procedure means that if each player in a two-player game has resolved Crafty Cutpurse’s triggered ability and one would create a token, it really will enter the battlefield under that player’s control. The token would enter the battlefield under player A’s control, so player B’s effect affects it. Now that token would enter the battlefield under player B’s control, so player A’s effect affects it. Each replacement effect has now been used, so the token will enter the battlefield under player A’s control.