Game Theory for Middle School Day 2: Chicken and Commitment

Chicken is a *discoordination *game, in which each player gets his highest payoff from making the move that the other player does not make.

We start, of course, with a video:

Then I go on to help the students build a payoff matrix. This is a good time to reiterate that payoffs are ordinal *and *approximate (the order from least to greatest is more important than the exact amounts). Notes:

  • The negative payoff from both guys swerving comes from the broken tractors and humiliation in front of their friends. You can make (and discuss) assumptions that adjust this payoff, but it should generally be worse than steady/swerve but better than steady/steady.
  • 13 year olds are little lawyers- they love to find loopholes and call you on them. It helps to teach these kids the word abstraction early in the unit: I explain that in order to just focus on the math and the theory, we're going to create a simple model of a complex situation.

Chicken payoff matrix

Discussion questions:

  • If you know the other person is going to swerve, what should you do? If you know they are going to hold steady? What should you do?
  • What should you do if you don't know what the other person is doing? Depending on the class level, you can introduce the idea of risk-loving, risk-neutral, and risk averse personalities. The former would hold steady, while the latter two would swerve.
  • What if you had the choice of swerving left or right? How would that change the matrix?

Then we get to the fun part: commitment devices, reputation, and meta-gaming. Given a scenario like chicken, what could each player do to convince the other one that he was going to hold steady? I love kids' answers to this- a few needed a little guidance, but all of these were independently generated at least once:

  • "He should just text while he's driving so he can't see the road. Then he won't know when to swerve so the other guy will just swerve."
  • "He should be drunk."
  • "He should be a badass so everybody knows he won't back down."
  • "He should rip off the steering wheel! Beast!"

Explain to the students that these are *commitment devices- *strategies we can use that commit us to a choice for us down the road (heh), forcing the other person to make their choice based on the one we committed to. If they're reasonably sure we'll hold steady, they will swerve. 

Next: Cuban Missile Crisis! Start by showing the clip below from 13 Days:

 

Then, as usual, make a matrix:

Cuban missile crisis chicken payoff matrix

Discussion questions:

  • Wait, this really happened? The US and Russia played a game of chicken with nukes?
  • What would you do in the USA's position? The USSR position?
  • What commitment devices could the countries have used ahead of time to ensure they won the game?

Extension exercises and questions:

  • Draw a payoff matrix for chicken with options to swerve left or right.
  • Is tic-tac-toe a game of chicken? Is it a discoordination game? Why or why not?
  • Can you think of any coordination games, where both players need to do the same thing to win?