Matching games and auctions
In class on Friday we looked at matching-games and today we looked at auctions.
You can see a recording of this:
Matching Games
For Matching games I started by asking you to come up with individual rankings for physicists to work with mathematicians and versa:
Using this we described potential matchings. In our particular case this always lead to a bad matching for Turing but this was nonetheless the only matching that was stable.
We then spoke about the Gale-Shapley algorithm which is a powerful yet simple tool for finding stable matchings.
Auctions
Today we started with another auction for a £5 note.
I started by asking you all to write down what you thought was the value of that £5 to you. Some of you assigned quite a high value (more than £5) and some quite a low value (less than £5).
After that I said that the auction would be that the highest bidder would win the £5 and pay the second highest bid.
This lead to a discussion about what the optimal bidding pattern was based on value. Tim, who “won” the £5 (and owes me £7) had a strategy based on the assumption that everyone would bid near £5 so his winning bid of £50 would work.
There are two theorems with the associated chapter, the first of which actually shows in expectation the optimal bid is to in fact bid your value.