The phrase "be game for" means to be willing to do something or to be up for a challenge. When looking for antonyms for this phrase, you may consider terms like unwilling, hesitant, uninterested, or unsure. These words suggest a lack of enthusiasm or a reluctance to participate. Alternatively, you could use phrases such as "unwilling to take on" or "not up for" to convey the opposite meaning of being game for something. Whatever words you use to express the opposite of "be game for," they should clearly convey the idea of being disinterested, unwilling, or hesitant to take on the task at hand.