Who wants power in The Tempest?

More than anyone else in The Tempest, it's Prospero who strives for power of one sort or another. It was a loss of power that led to Prospero being banished to a remote island. Back home, he was the Duke of Milan. But because he neglected his duties to spend time with his books and his magic, he was usurped by his brother Antonio and cast adrift at sea.
Once established on the island, Prospero tries to reclaim some of his old power by controlling Ariel and Caliban. Having been deprived of earthly power, he resorts to the power of magic to exert authority over his new subjects. Although he treats Ariel somewhat better than Caliban, Prospero never hesitates to make it clear to the tricksy spirit just who is in charge.
So long as Prospero is deprived of what he believes is rightfully his—the duchy of Milan—he will continue to exercise power in his own way, combining the authority of a nobleman with the magical powers of a skilled sorcerer. It is only when he is eventually restored to his throne that he finally renounces his magic and consigns his books to the sea.