The World Just Keeps Getting Better
I lost my watch. I wanted to replace it with the exact same model, because I’ve memorized the the pushbutton sequences and I don’t deal well with change. So I went down to the Wal-Mart where I’d bought this watch, oh, probably about six years ago, but Wal-Mart, which deals with change better than I do, had “upgraded” to a more fashionable selection.
So how do you shop for a Casio watch without knowing the model number? And how does your answer change if I tell you that Casio makes over 1000 models?
Answer: You spend about a minute and a half on Google and discover a site called dealtime.com, which knows about every one of those models (and of course about a gazillion other watches from about a gazillion other makers too). Dealtime asks you a bunch of questions about the watch: Digital or analog? Casual or dressy? Square face or circular face? It brings up a page with pictures of the 32 models that fit your criteria. There in the middle of the page is your watch.
You click on the watch, and dealtime brings up a list of five websites where you can buy this model, in a neat little chart showing prices and customer ratings of the sellers. At the top of the list is etronics.com, offering your watch for $14.99. Two days later, you have your watch.
All that technology to sell me a fifteen dollar watch! Oh, God, I love the web.
Markets in Everything
No comment necessary, I think:
http://cgi.ebay.co.uk/ws/eBayISAPI.dll?ViewItem&category=324&item=5527273221&rd=1
Quantum Game Theory
Let’s play a coordination game: You and I are each asked a single question, either “Do you like cats?” or “Do you like dogs?”. Our questions are determined by independent coin flips. We both win if our answers differ, unless we’re both asked about dogs, in which case we both win if our answers match.
Here’s a pretty good strategy we could agree on in advance: We’ll contrive to always differ. Whatever we’re asked, I’ll say yes and you say no. That way we win 3/4 of the time.
Can we do any better? No, if we live in a world governed by classical physics. Yes, if we live in the world we actually inhabit—the world of quantum mechanics.
All we need is a pair of entangled particles, easy enough to create in the laboratory. If I get the cat question, I’ll measure my particle’s spin (which is either up or down) and answer “yes” or “no” accordingly. If I get the dog question, I’ll do the same thing, but first I’ll rotate my measuring apparatus by 90 degrees. You do the same, but start with your measuring apparatus rotated 45 degrees from
mine.
The thing about entangled particles is that the outcomes of these measurements are correlated in a very particular way, and remain so forever, even if the particles are separated. In particular, our answers will differ about 85% of the time unless we both make “dog” measurements, in which case they’ll agree about 85% of the time. Overall, then, we’ll have about an 85% win rate. Those particular correlations would be impossible to achieve with any set of measurements if our electrons obeyed the laws of classical physics.
(More precisely, our win rate is cos2(pi/8).)
I took this example from a beautiful paper by Richard Cleve, Peter Hoyer, Benjamin Toner and John Watrous. (The paper has a lot of other cool examples too.) The moral is that game theory changes dramatically when players have access to quantum technology—which might sound very science fictiony at the moment but probably won’t in another couple of decades.
More on Vaccines
Though Alex has already blogged about the Kremer/Snyder paper on vaccines versus cures, there are, I think, a couple of comments worth adding.
According to Kremer and Snyder, monopoly sellers would rather sell cures than vaccines. To get this result, they need some heterogeneity: we all have different probabilities of getting sick (though we all find it equally costly to get sick).
But what if you introduce the opposite kind of heterogeneity? (That is, we all have different costs of getting sick, even though we all face the same probability of getting sick.) Then it’s a nice little exercise for your students to show that the cure and the vaccine are equally lucrative monopolies (ignoring the positive externalities of the vaccine).
A more important observation: In the Kremer/Snyder setup (still ignoring positive externalities), it’s a good thing for sellers to invest in cures rather than vaccines. The reason cures are more profitable is that they in essence allow perfect price discrimination. So with cures, there’s no deadweight loss due to monopoly; with vaccines there is.
The analysis changes if you assume, say, that a vaccine prevents a four-day illness, but a cure only cuts two days off your illness. Then vaccines might or might not be socially preferable to cures—but in that case, willingness-to-pay for vaccines versus cures would double. This gives sellers an incentive to produce vaccines. The incentive isn’t perfect, but it goes in the right direction.