Game Theory for Middle School Day 1: Payoff Matrices and Rock Paper Scissors

I majored in Economics with a focus on game theory, so I like to share it with my kids. I usually spend anywhere from a day to a week on the subject, depending on the students' engagement. Because Econ often seems dry to younger kids, I like to jump them right into the middle, and deal with terminology later on  in the unit. For today, the objective is mainly to understand how situations can be reflected in a payoff matrix.

1) Have the kids play rock-paper-scissors.

2) Ask what strategies they use to win (eg "play what would beat the winning move from the last throw."  Ask their friends what they would do if their opponent was using a particular strategy. Introduce simultaneous vs. turn based games. Discuss how much RPS would suck as a turn-based game.

3) Construct RPS payoff matrix. Fill in a few squares; have them do the rest.

Rock paper scissors payoff matrix

4) Play videos:

 

Discussion questions:

-How good are these guys? Is this a real game?

-Who's paying for the $50,000 cash prize? (students will notice the heavy Bud Light signage all over the stage)

-Does the cash prize make sense, given what other pro athletes are paid?


 

I like to have them generate their own payoff matrix or decision tree for the game, but if they need a static visual aid, here's a good one:

image from upload.wikimedia.orgDiscussion questions:

-Is this game as balanced as normal RPS? Why or why not? Do you think it would be more fun? Why or why not?

-Is this game easier or harder to create strategies for than normal RPS?

-What would a payoff matrix for this game look like?

If there's time in the period, we spend it talking about random situations in life we could model with payoff matrices. I also try to get them thinking about the complexity of games like chess, and why can't solve those on paper.