 This video will help to introduce the idea of Bayesian games, which is a new game representation. So here I want to think about auctions. Now, canonically, when we think about auctions, we think about something like this wood cutting from 1885, showing the auction of tea in Melbourne, Australia. We've got a guy in a top hat standing at the front of the room, and he's got a gavel in his hand, and he's probably talking in a funny voice, and at some point he bangs the gavel and somebody just won a bunch of tea. But auctions are a really practical thing. They really are quite important in the world, and they're used for a lot of different things. Here's an example of a much more modern auction. This is an auction of bluefin tuna at a fish market in Tokyo, and you can see this is from 2008, and auctions are used to sell fish because fish spoil quickly and their value changes quickly. So it's important to find a way of determining what the prices should be on a day-by-day basis. Here's an auction by the US Marshals Service selling some horses that were seized by somebody who was convicted of embezzling money, and so the US Marshals got a bunch of guys in cowboy hats to round up this person's horses and sell them off to recover some of the embezzled money. Again, you can see why an auction might be used here, because the value of something like a horse is pretty unclear. It depends on supply and demand. It depends on intangible things like the value of the horse, the number of other good horses on the market at a given time, and so on. Here's yet another auction. This is an auction of rugby players, presumably only for a limited time. And again, you can see why an auction might need to be used, because it's pretty unclear what this guy would be worth. Of course, not all auctions happen in person. Here's a famous auction that occurred on eBay a few years ago. This was a situation where a woman in Florida was eating a grilled cheese sandwich that she had made for herself. You can see a picture of it right here. And she took a bite out of it, and then she was amazed to discover what she considered to be a perfect likeness of the Virgin Mary in the shape of the burn mark on the grilled cheese sandwich right there. And so she was so amazed, she decided that this was a religious relic. She stopped eating the sandwich. And like anyone would do if they discovered a sign from God, she posted it on eBay to sell to the highest bidder. This is kind of interesting, both because it's ridiculous, but also because it goes to show how the internet allows auctions to create markets in places where they really wouldn't have existed before. So if this had happened before the internet, it seems pretty clear that this woman would have had a hard time finding a buyer for her grilled cheese sandwich. But you can see that when I took this screenshot, the auction still had almost four days to go, and already the top bid was 7,600 US dollars. And this really was not a hoax. This was an actual auction. It was covered in the news. So that's kind of an amazing thing. It goes to show the power of auctions to match up buyers and sellers. Here's the last auction picture I want to show you. This is what's called a silent auction in a charity auction. So what's going on here is there are actually two different bundles for sale. So there's a gift basket here for sale, and all of the people who are interested in buying it are able to go up and inspect it, decide what they think it's worth to them, and then they write a bid. They write their name and amount that they're willing to pay on this sheet of paper here. And the reason that I think the silent auction is particularly interesting is we can really see how this might look like a game. We here have a well-defined action space. You come, you look at the piece of paper, you can see the moves of the players who have moved before you, and then you take an action which is choosing to write down a number. And at the end, presumably you don't write down a number that is worth more than the gift basket is worth to you. At the end, if you have the highest number, you win the gift basket. You realize an amount of utility which depends on how good the gift basket is from your point of view, and you pay whatever amount it is that you wrote down on the piece of paper, which is presumably less, and you get the difference as your utility for having played the game. So all of this looks like something we can really model in the context of this course, and if we realize we can model the silent auction this way, we can probably see that we can model the other auctions that I've just described in this sort of way as well. However, there's something really critical about the case of the silent auction, which is different from the games that we've talked about in this course already. And that is that when I want to reason about what other people will do in this game, I need to think about what they think the gift basket is worth to them. That's going to be something very important to the way they choose to act in the game. And critically, this is something that will affect their utility, and it's not something that I know. And so this is a case where I'm not quite sure what other player's utility functions are, even in cases where I can imagine what all of the actions taken in the game are. So this is a different sort of setting than we've ever looked at before, and hopefully you can see that this is really necessary to model the case of auctions. It's really fundamental to an auction that I'm not quite sure what the good is worth to all of the other participants in the auction, and that fact is really critical to my strategic reasoning in the auction. So Bayesian games are a formalism that allows us to model this kind of uncertainty, uncertainty about the utility functions, and this week we'll go into Bayesian games in more detail.