Overview
The Hunger Game is a Blood and Wine secondary quest that follows La Cage au Fou. Forty-eight hours after Geralt brings Marlene de Trastamara, the former spotted wight, to safety at Corvo Bianco, the quest begins on its own. If Geralt simply meditated on the estate, he may need to leave the grounds first.
Where will Marlene go?
Marlene is feeling better, but her whole family died long ago and she has nowhere to go. Geralt can suggest that she go to the city and start over, which ends the quest, or invite her to stay at Corvo Bianco. Letting her stay counts as a Proof of Compassion for There Can Be Only One.
The dowry
If she stays, Marlene is delighted and promises Geralt a hot meal whenever he comes home. She also tells him about a dowry her father once set aside for her. Since she never married, she wants him to have it. Travel to the Trastamara Estate Ruins and go down to the room whose floor is covered in spoons. The dowry is in the second barrel from the right as you enter.