The phrase "being game for" typically means being willing or enthusiastic to participate in something. Its antonyms include being hesitant, unwilling or uninterested. Being unwilling suggests a lack of desire to participate, while being hesitant suggests a reluctance due to fear or uncertainty. Additionally, being uninterested suggests a lack of enthusiasm or passion for the activity in question. Other antonyms for "being game for" could include being apathetic, disinterested, or simply indifferent. Ultimately, if someone is not "game for" something, they are not fully committed or excited about the prospect of participating.