What motivates Odysseus to risk his life and the lives of his men in The Odyssey? What price does he pay for his adventure?
I think there are a few things that motivate Odysseus to risk his life and the lives of his men.
First, I believe that he really wants to get home. He truly feels love for Penelope and loyalty towards her. Otherwise he would never have left Calypso's island.
Second, I believe he is motivated by the desire for glory. Heroes in Homer's work tend to be motivated by this. You can see this when Odysseus taunts the Cyclops as he and his remaining men flee. He wants the Cyclops to know his name and spread his fame.
He pays a price -- he gets lots of his men killed and he himself has a hard time and encounters lots of danger.