In a negotiation, players will never get less than their added value.

The theory predicts that players will never get more than their added value (or their added value as perceived by the others in the game). But the question asked about getting less than their added values. It is quite common for players to get less than their added values. In the first problem we saw with Abe and Bea, both players had an added value of 6—without either of them, the pie disappears—but we can’t give them each 6 since there is only 6 to go around.