Paper, Scissor, Rock!

A teacher was having trouble getting her students to learn their facts, but she noticed that her students often played the game "Rock, Paper, Scissors". She made a game with similar rules in order to encourage the students to learn their facts.
The class would be divided into three teams: Rock, Paper and Scissors. The teacher would ask the students a question and the class would raise their hands if they knew the answer. If the first person to answer the question correctly is in the Rock team, he or she would choose one player from the Scissors team to be eliminated. Similarly, if a player from the Scissors team was first to answer the question, then he or she would eliminate a member from the Paper team. Lastly, if a player from the Paper team was first to answer correctly, he or she would eliminate a member from the Rock team.
The teacher would then continue asking questions until only one team still has members. That team would be declared the winner and all its members would win a small chocolate.
However, as soon as she explained the rules to the class, one particularly smart student immediately found a large flaw that made the game unplayable. Can you do the same?


After one team loses all its members, the team that it eliminates members from will always win. For example, say the Scissors team is the first team to lose all its members. It is now impossible for the Paper team to lose any members, but the Paper team can still eliminate members from Rock team, so it will eventually win (if the Rock team answers questions, there would be no one left for them to eliminate so nothing would happen). This means that the best strategy is actually to avoid answering questions until one team is eliminated. If all the players know this, the game would never end.