The Hunger Game is a secondary quest available in the Blood and Wine Expansion. Quest theoretically starts after bringing Marlene to safety at Corvo Bianco and feeding her. But it cannot be unlocked by simply meditating a few days. The quest seems to launch once Geralt begins the main quest Wine is Sacred by visiting the Beauclair Palace to talk to the duchess. Alternatively, any act of updating a quest after 24 in-game hours seems to launch the quest as well.