This experiment is fairly theoretical, on whiteboard maths, your challenge when demonstrating is to make it hands on! Make sure you play out some of the games.

When talking of game theory we really all need to be on the same page about what a game is. What do games have in common?
All games have players, how many might change but we really need at least one player to make it a game.
Winners and loosers, in a sense we should always have this. Even cooperative games we have everyone winning together. Winning is quite complicated and we're going to model it using points. We'll stick to a convention that positive points is good and negative bad. You could view these as money but we'll think about them just as generally good or bad things.
Actions, it wouldn't be a great game if there weren't any choices to make for one player.

There are other things some games have but others don't, E. G. Dice, chance, skillz, etc. Rock paper scissors is a good example of a game with none of these, imagine your playing over who has to do the washing up may give you better insight to why the looser gets negative points.

Prisoners dilemma
Both players are prisoners and have been taken to different rooms to talk to investigators, they have two choices. Stay silent or snitch on their accomplice. They've been promised a deal for snitching reducing their jail time by a whole year, however the extra evidence won't look good on the other person. If they both stay silent they'll each get a year, if one snitches and one doesn't the snitch won't go to prison but the other gets three years, if both snitch they'll each do two years.
You can see both staying silent seems best for the group, however for the individual is always better off going for snitch, look at the options and no matter what they spend a year less in jail for snitching, the deal they're offered is true! We call snitch snitch the Nash equilibrium.
There's on problem with this model, people may have said 'snitches get snitches', in this model you'd get 0 years of prison and stitches, which are a big negative number to offset the equilibria.
This is a coordination game, its best when people say the same thing.
The other option of both silent is the optimum, however it's not stable to the other playing changing to snitch! This means this is not a Nash equilibria.
There is only one Nash equilibria, we call this a pure strategy equilibria too as players never mix between moves.
You could reskin as the nuclear war arm or diasrm game tooo.

Chicken
(if anyone can give a better setting of this game please do)
Both players are driving at each other, they can keep straight or swerve. They get 0 points if both swerve (both chicken), if one swerves one straight then the server gets - 1 for being uncool and the straight 1 for coolness, if they both go straight they crash and die, this is minus a million, each, as its bad. This is anti coordination, players want to say the opposite. There's two Nash equilibria at both opposite points. In fact there's a range of 'non-pure' strategies where you pick at random between swerve and straight. One way to do better is by Symmetry breaking, we could play this game as a choose the side of the road to drive on.we break Symmetry by agreeing a Time.

There's more games if you want.