Spy game

If person A were the spy, all 3 people would be telling the truth, which is impossible since one liar is included in the group.

If person C were the spy, all 3 people would be lying, which is impossible since one truth-teller is included in the group.

So person A is the liar, person B is the spy (who is lying), and person C is the truth-teller.

If the liar is person A, he is lying when saying that he is the spy. The spy can say either the truth or lie, and in this case he lied when he said that the liar is the spy. The spy is person B. The truth teller tells the truth when he says that he isn't the spy. If the spy was Person A, then everybody would be telling the truth, which is what the liar doesn't do. If the spy was Person C, everyone would be lying, which is what the truth teller doesn't do. So the spy is person B.

Statements by A & B are in corroboration, which means the two are on the same page in truths or in lies. But with the statement by C which didn't seem to be directly contradictory to the other two, we noticed that that doesn't make any sense since a knight and a knave could never agree on anything. Thus, we are led to believe that C must have a different truth value than the others, and as such, C must be either a knight or a knave themselves. With the establishment of this fact, then C's statement must be the truth. A and B must have lied, and that makes B the spy and A the knave.