We study distributed choice of retransmission probabilities in slotted Aloha under power differentiation. We consider random transmission powers and further study the role of priorities (through power control) given either to new arriving packets or to backlogged ones. We study both the cooperative team problem in which a common objective is jointly optimized as well as the noncooperative game problem. We show that the new proposed schemes not only improve the average performances considerably but are also able in some cases to eliminate the bi-stable nature of the slotted Aloha.