2. Since the probability of A and B is the same, A can be used to represent A and B, and B can be used to represent C. Asking the loser in the second game is actually asking the referee in the third game. I assume that A (A or B) is used to represent the referee of the third game, that is, the loser of the second game is A (A or B), then the third game can be expressed as A B A, and you can infer the situation of other games accordingly. Anyway, according to this situation, it is absolutely impossible for C to be a referee three times.
To sum up, the referee in the third game is B, that is, C, that is, the loser in the second game is C.
I hope it helps you!