Curse of Oblivion is one of a cycle of new cards in Innistrad that enchants a player. This curse causes the enchanted player to exile two cards from their graveyard at the beginning of each of their upkeep steps. The choice of which cards in this players’s graveyard to exile is made by the enchanted player. It does not matter that the curse is controlled by another player. This ability does not specify that the enchantments controller chooses which cards are exiled therefore the affected player will make the choice.

Also, if there are not two cards in this player’s graveyard the enchanted player will do as much as possible and exile what they can. In other words, if there is only one card that care will be exiled.