Facilitator notes: not student-facing. These notes are for planning and running classes. Student resources are at vknight.org/gt/.

Matching Games

Activity (20 minutes)

Goal. Elicit preferences and motivate the need for a stable matching.

Use this preference sheet and ask students to work in groups to identify preferences for each mathematician and physicist.

Arrive at this:

Mathematicians

Physicists

The following will obtain a stable matching:


import matching
import matching.games

mathematicians = [
    matching.Player("Gauss"),
    matching.Player("Noether"),
    matching.Player("Turing"),
    matching.Player("Euler"),
]

physicists = [
    matching.Player("Einstein"),
    matching.Player("Curie"),
    matching.Player("Newton"),
    matching.Player("Feynman"),
]

gauss, noether, turing, euler = mathematicians
einstein, curie, newton, feynman = physicists

gauss.set_prefs([curie, newton, feynman, einstein])
noether.set_prefs([curie, feynman, einstein, newton])
turing.set_prefs([feynman, curie, einstein, newton])
euler.set_prefs([newton, curie, einstein, feynman])

einstein.set_prefs([noether, gauss, turing, euler])
curie.set_prefs([noether, euler, turing, gauss])
newton.set_prefs([gauss, euler, noether, turing])
feynman.set_prefs([turing, noether, gauss, euler])

game = matching.games.StableMarriage(mathematicians, physicists)
game.solve()

Discussion (20 minutes)

Show students the notes, when you get to the algorithm work through the algorithm with the students.

From the activity to the exam answer

The activity above is written up as a marked exam question: Question 1 (the in-class activity) on the Matching Games page, with a full worked solution. Closing the loop here is the step that helps students who find exams hard: work through that question together, or set it as the immediate follow-up, so they see the game they just played turned into a full-mark answer.

Communications

General email templates to send before and after this class. Fill in the bracketed placeholders before sending.

Before class

Hi all,

A reminder that our next Game Theory class covers Matching Games.

All of the course materials, including the relevant chapter, are available
at https://vknight.org/gt/. It is worth skimming the chapter beforehand.

See you in class,
Vince

After class

Dear all,

Thanks for your work in today's class on Matching Games.

A recording is available here [RECORDING LINK] and on Learning Central.

All class resources are available at https://vknight.org/gt/.

Thanks,
Vince