Fixing a Game Theory Activity

[ch3cooh]

I taught a class tonight that didn't work. It was somewhat fun, and somewhat well developed in presenting applications of game theory. But overall: :P I'm writing this post to note down thoughts before I forget, and I'm making it public because I generally think that various try-fail-learn processes should be more open/public. Also, I've been feeling awkward lately that I present myself so unilaterally as an 'experienced teacher' now, and not a student/new and learning teacher or in any other mind-set... more on that in the future perhaps.

I've decided to try for 2 focus goals of self-improvement in teaching each season. This season, my goals are (1) Time management via consciously prioritizing academic and non-academic goals, and (2) creating situations where my students feel ownership for what they're making.

Game Theory part III of IV

This activity was part of a 2 hour session for 45 students in 6th-8th grade.
1) The students cut out paper candy bars and then ranked each type (30 types) of candy bar 0-3 so that the sum of all of the types was 50.
2) In groups of four, I asked them to design an agreed 'fair' method for distributing the candy
3) They implemented the method, and the person to get the most total value of candy (using their own value sheet to scale) in each group, wins a real prize.

Time management went OK. I cut the activity a bit short (~1:15 total out of the 2 horus for the session) and extended some other parts of the class that were working better.

Review: Freedom to Experiment is one of the four foundational freedoms that I strive for when I teach (the 4 are: freedom to fail, experiment, of effort, and to try on different identity roles). But in order for an activity to feel like a valid experiment, there needs to be meaningful choices that the students understand when they are making those choices, and there needs to be feedback, ideally interesting, immediate feedback in response to their choices, and then a chance to go back and make those choices again, more informed. Here's where I think I went wrong:

1) Part 1 mechanics: there were too many types of candy and the max rank wasn't high enough. It should have been something closer to 6 types of candy, 15 points total, rank each from 0-10 I think.
2) Part 2 mechanics: I should have gone over more examples before setting students out to make their own. They had a lot of choice here, and I wanted them to have 'ownership' of their methods, but only a few groups really seemed to construct - most just fished around for something reasonable-seeming and then used that.
3) Part 3 mechanics: OK, but I should have had a sheet for describing more data about the results of using the algorithm -- showing which kinds of preferences or strategies would have the advantage and how and why.

Next time:
I think I should have had a first part of class dedicated to working with 3 or 4 very different division algorithms, letting students get a feel for which are best in different circumstances. Then part 2 could become combining these methods to make something more fair for everyone. Part 3 needed more organization, some follow-up questions with exact answers in addition to the . And I should have left time to play a 2nd time, without letting people change their ranks in-between, to illustrate the impact of making preferences public.

Unexpected:
I spent 10-15 minutes in a few random blocks telling stories about how game theory has come up in scenarios I've seen:

Real estate needing to buy all of some set of houses in order to make any of those houses valuable, a sport conference leader needing to choose a mechanism for coaches drafting their teams, the Splash class lottery algorithm that I worked on as a college student, etc.

These stories hushed the room, and I think I could do more with them. I could ask students how they would 'game' each system, and then how to patch those gaps to make that kind of 'cheat' impossible.

Next time:
1) Real-life game theory examples
2) Trying out 3 or 4 simplified algorithms in groups of 4, with a smaller candy-set
3) Give groups time to build one algorithm from the existing ones
4) Have students implement it
5) Discuss what students chose to do and who it advantaged
6) Play again
7) Discuss the result of more-public value information

Big picture -- If I can make this class into a really excellent one, I think it would make a great introduction to the game theory sequence I've been building. I'm working on 8-12 class sequences right now, of sessions that can stand alone if they need to, but that tie together under a theme as well.

A) Designing Something Fair -- Real Life Game Theory, Types of Fairness
B) Designing Something Fair -- Pet (instead of candy) Intro
C) Designing Something Fair -- Design your own fair division algorithm
D) Designing Something Fair -- Fair Voting Lab

E) Comparing Strategies -- Monty Hall Intro
F) Comparing Strategies -- Prisoner's Dilemma (Iterative Play AI Design)
G) Comparing Strategies -- RPS and Rock Scissors (Mixed strategies)
H) Comparing Strategies -- Real life Game Theory, Nash Equilibria

I) Perfect Play -- Say 16
J) Perfect Play -- 2-pile Nim (poison points)
K) Perfect Play -- Dots and Boxes
L) Perfect Play -- Dots and Boxes AI + Tournament

Higher level Topics:
* Advanced Combinatorial Game Theory
- perfectly logical pirates
- proofs about combinatorial games
- gomoku and variants