Prepare by teaching the main question as well as full sentence answers: "Yes, you may. / No, you may not.". Remind the students that "mayn't" is absurd and should never be used. Also, go over the concept of "Liar!!" Write it on the board with 5 marks undernearth it. These will be used later. I like to have the students repeat it with a little anger as well as in a louder voice. It helps get the point across that it is a negative thing and shouldn't be taken lightly.
Gather 5 students at the front of class. Give each a slip of paper with either an 'X' or 'O'. 'X' corresponds to "No, you may not." 'O' corresponds to "Yes, you may." They are allowed to give Yes or No answers regardless of their paper. There should be only one 'O' and four 'X' in the bunch. This is the lying team.
The left over students stand up and ask an individual on the lying team, "May I sit down?". If yes, sit down. If no, stay standing.
If the asking student feels the answering student is lying, they can call out "LIAR!!" and we must check the slip of paper. If the previous answer matches the student's paper, they are not lying and the asking team loses one point (the marks on the board). If the answer does not match, it is a lie and the answering student must sit. Take one 'X' card out of the bunch. After a student calls "Liar", the cards should be mixed up and redistributed to the lying team.
When there is one student left on the lying team, have them choose between 'X' and 'O' cards each time a question is asked.
If the lying team all sits, the asking group wins. If the asking group loses all their points, the lying team wins.
P.S. - You may have the situation when all the students sit down even if there is no winner yet. It is up to you what to do next. I like to change the pattern to "May I stand up?".