Monthly Archives: June 2010

The Shubik-Bazerman Auction

Today I will introduce a baffling piece of economics, psychology, or game theory, which has been called the dollar auction, though I consider that a bit of a misleading name. I believe Martin Shubik was the first to introduce it as a thought experiment, and Max Bazerman is the only person I have found who carried it out in practice. So I will dub it the Shubik-Bazerman auction for the time being.

A $20 bill is up for auction according to the following rules.

  • The bidding starts at $1 and goes in exactly $1 increments, and it is not allowed to bid twice in a row.
  • The two highest bidders pay the full price of their bid, but only the highest bidder wins the $20.
  • There is no communication allowed other than bidding.

A handful of people open bids for the $20. “Whatever, it’s just a bid, it couldn’t hurt, and I can drop out any time I want.” By the time the bidding reaches about $10 all but two contenders drop out — and the top two realize that they will either win the $20 or shell out cash to the auctioneer. Around $16 they seem to realize what is happening: the auctioneer is going to make a profit, and one of them is going to make almost nothing while the other pays almost $20.

Finally, bidder A bids $20 for the $20 bill. The immediate options available to bidder B are: drop out and lose $19, or bid $21 for the possibility of only losing $1. The hope of mitigating losses causes bidder B to bid $21 for a $20 bill. Bidder B is confronted by a similar dilemma, and bids $22. This continues for some time. Seven times (of 180) the bidding has cleared $100.

This phenomenon fascinates me, and I have tried in vain to formalize it. Say you are already above $20 and are considering making a bid. Your (unconscious?) thought process may be something like: he will surely drop out before he bids 10 more times, because this is ridiculous, at which point I will lose less than I would if I dropped out now. After all, 20 bids is a long time and it’s hard to see paying that much more for a measly $20 bill. But this thought process is going through both parties’ heads (perhaps unknowingly), so 20 more rounds continue without one dropping out. And the idea is continuous: neither really has a hard cut-off in mind, but each is playing as if the other has a hard cut-off in mind (and assuming said cut-off is reasonable, then they are both playing optimally).

Assuming you accidentally engaged in such an auction (say for $1), how could you ask mathematics what to do? What is the best strategy assuming you are playing against your own strategy (this strategy must work whether you were the first or second bidder)? A simple solution is to stop immediately and share the money with the other bidder, but let’s define that away and assume that the winner keeps all the money. Are the given conditions a guaranteed loss? If so, isn’t it fascinating that one can “give away” $20 and, under so-called “rational” conditions, not expect to lose any money?

What are readers’ ideas about how to analyze this? Do any interesting analogies come to mind?

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Flattr

I just signed up for Flattr. I requested an invite two days ago. That was fast! I like the idea — commit yourself to, say, $10/mo for paying for freely provided online entertainment, because it reinforces that you are a good person. And then just click to donate, and you don’t have to worry about not eating next month because you donated too much. There is so much wonderful content available freely online, and I want to donate — money is just hard to part with, you know? So this is a very interesting solution.

You will notice a flattr button in my blog sidebar. This is fairly easy to do with wordpress.com blogs, even though they say they have no plans for a flattr widget. When you submit a new flattr page, you get some code for the button, which will look something like this:

<a href="http://flattr.com/thing/18655/Luke-Palmer-functional-programming-and-mathematical-philosophy-with-musical-interludes" target="_blank">
<img src="http://api.flattr.com/button/button-static-50x60.png" alt="Flattr this" title="Flattr this" border="0" /></a>

Add an image widget to your sidebar with the second URL (http://api.flattr.com/button/button-static-50x60.png) as the image to display and the first URL (http://flattr.com/thing/...) as the link. Tada!

Humanfood

I am insomniatic, so I’ll write about what is keeping me up.

I want to concoct a “humanfood” for myself: a food that would keep me healthy even if it were 100% of my diet. I spend energy every day worrying about what I should eat and traveling around town to get it. Sometimes I get in a rut and just eat Subway every day (there is one across the street), which is gluten-heavy and probably incomplete in a few ways. This contributes to my malnutrition and pushes me further into my rut.

I understand that nutrition is a subtle balance, but mostly I am trying to protect myself from malnutrition. I trust my body to do a pretty good job sorting out the jewels from the junk (as long as there isn’t too much junk, which I am typically good about). As I am coming to understand how tightly coupled my motivation and energy level are to my nutrition, I conjecture that having some prepared food that I can snack on anytime and get my nutrients for the day will help me get more out of my time.

And yet, I don’t want to be a nutritionist. Thus humanfood.

Fortunately my mother is associated with people who spend a lot of time thinking about nutrition. I’m going to start by asking them, and doing research on the interwebs. If any of my readers have ideas for what would make good ingredients, do post. Please, keep it reasonable though — this is something that I am thinking about eating all the time, so I require more than just for it to be healthy. It should be “maximally healthy”. (Calories are important too!)

I will publish my research and experiences as I acquire them. I will try to keep my reports relatively scientific, but I’m trying to get on with my life in the meantime, so I probably won’t be able to do that to an extreme. In other words, I will try to make my anecdotes worthwhile.