Game Theory – It Takes Balls

April 30, 2012
Posted by Jay Livingston
Cross posted at Sociological Images

I don’t know much about game theory.  I’ve always found it hard to squeeze real-life situations into the shape of a prisoner’s-dilemma matrix and to think of life as a game.  A game show, on the other hand, is a game.  And the final round of the British show “Golden Balls” is totally Prisoner’s Dilemma.  (Shouldn’t that apostrophe be moved to make it be Prisoners’ Dilemma? After all, it’s not solitaire.)

You can get the idea of the set-up in the first two minutes of this clip.*  But don’t stop there.  Watch the full six minutes, and appreciate the ingenuity of the strategy played by Nick (he’s the guy in the brown shirt on the right of the screen).

SPOILER SPACE, which I’ll fill with the “Golden Balls” matrix.

In many prisoner’s dilemma scenarios, the prisoners are separated and can’t discuss their options.  In “Golden Balls,” they can talk things over, the only catch being that each player is well aware that the other might be lying.  Earlier rounds of the game are designed to encourage lying. 

Nick is ingenious in two ways.  First, he brings in an option that “Golden Balls” does not include but cannot exclude: the offer to split the loot 50-50 after the show even if the show gives the entire amount to him.

Second (and here is where my lame game-theory knowledge is showing), by convincingly maintaining that he is going to Steal, he destroys the Nash equilibrium that “Golden Balls” tries to create.  He forces Ibraham to choose Split, for Ibraham’s position n ow becomes this:

• If Nick is fully telling the truth about sharing: Split, I get £6500. Steal, I  get 0
• If Nick is lying about sharing: Split, I get 0.  Steal, I get 0.
• So my only hope of getting anything is Split.  

Which is what he does. 

Nick’s ploy also creates an interesting dramatic switcheroo for the viewers as well.  As we watch the clip, it looks as though all the pressure is on Ibraham.  We can see him debating with himself and with Nick.  But after the two men show their balls, we realize that in reality, it’s Nick who had to be sweating, not about which choice he will make – he has already decided that – but about whether he is actually fooling  Ibraham.  He was betting £13,000 on his own acting ability.  That takes balls.

One other observation: I used to watch “Survivor,” and when players would lie and succeed, I might have admired them for being the clever strategist, but I didn’t like them.  In fact, I often actively disliked them.  But here, when I found that Nick had lied successfully, I was hoping that Ibraham or “Golden Balls” would give him a few extra pounds as a bonus.

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* The clip is from February.  I found it thanks to  Planet Money, which posted it last week without comment.

Weed Arrests Are Not About Weed*

April 29, 2012
Posted by Jay Livingston

Arrest data for some crimes rise or fall with the amount of that crime.  If you see arrests for homicide increasing, you can be fairly sure that homicide itself is on the increase.  By contrast, an increase in arrests for prostitution is almost certainly the sign of a “crackdown.”  A higher level official – the precinct commander, the police brass, maybe even the mayor – has told the cops on the street to arrest more hookers. 

Neither of these explanations accounts for the trend in marijuana arrests in New York, particularly in the Bronx.  On Sept. 19, 2011, Ray Kelly, the NYPD commissioner, issued an order that police should not arrest people for possession of small amounts of marijuana, the personal-use weed that cops found in stop-and-frisks. 

The Guardian has published some graphs (here) showing the numbers of marijuana arrests in 2011 and in the previous three years.  These usually decline in the fall – cooler weather, back-to-school – and the Kelly edict should have steepened the slope.  But that’s not what happened.

(Click on the chart for a larger view.)

Keith Humphreys at The Reality-Based Community notes that marijuana arrests are often “substitute arrests.”  Just as a substitute drug is what you use when you can’t get the drug you want, a substitute arrest is one cops make when they can’t arrest the person for the crime they’d like to bust him for.   The cops might be doing whatever they can to punish someone witnesses might not want to testify against – a high-level drug dealer, a frequent wife-beater, or even a robber. Or the cops might be using stop-and-frisk marijuana arrests to get troublemakers off the street, at least temporarily, in order to maintain order.  Or they may be using the arrest to assert their authority (or from the arrestees’ perspective, throwing their weight around by hassling kids). 

“Substitution arrest” may be good explanation for why police bother to make these one-joint arrests.  But it does not account for the increase in such arrests following an order from the top to stop doing it.

I’m puzzled.


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*The title of this post is derived from one of Robin Hanson’s favorite constructions   I’ve used it before (here), and I’ll probably use it again.

We Want to Have Our Appendix Out Too

April 26, 2012
Posted by Jay Livingston

How compatible are medical care and the free market?

The SocioBlog’s most viewed post (it got Boinged) showed widely varying prices among countries for the same medical products (hospital stay, Lipitor, OB delivery, office visit).  The US prices were four to ten times higher. 

Within the US, even within the same county, prices also vary widely.  Sarah Kiff at WaPo’s Wonkblog reports (here) on a study in the Archives of Internal Medicine (gated, here) that compared prices for an appendectomy.  The range: $1,500 to $187,000.  It’s as though the price of haircut ranged from $15 to $1870.   Even in the county with the least variation, the difference between the least and most expensive was $46,000.

It’s essentially the same service, though one haircut or appendectomy might be much better than another.  But not that much better.  These prices suggest that the usual market processes are not in play.  And they are not.  When I get a haircut, I pay the barber, and I check the price list before I go into the shop.  If my haircut insurance company were paying, I’d just walk in.

Also, unlike an appendectomy, my haircut is not an urgent production.  My untrimmed hair is not causing me to double over in intense pain, desperate for relief.  Even if I don’t act quickly, I won’t die.  I can take my time to shop around.  I can ask friends for suggestions, I can look for online reviews, and afterwards, I can form a reasonable opinion of the barber’s competence.  I’ve never had appendicitis, and unlike Miss Clavel's charges, I’m not eager for it.  But if my appendix were to start acting up, I’m sure I would not be a Consumer Reports type of consumer. 
 
The market is supposed to bring us more and better goods and services at a lower price.  With healthcare in the US, both the process and the outcomes suggest that this is not the ideal example of a market.

My Lunch With Charles

April 25, 2012
Posted by Jay Livingston

Charles Murray is the first author Nicholas Lemann discusses in his New Yorker piece (here) on inequality.  Murray’s recent book Coming Apart documents the moral decline of the white working class, and while Lemann doesn’t dispute Murray’s data, he is puzzled by Murray’s choice of villains – the liberal elite. They may live exemplary lives – work, family, religion –

But, unlike the elite of Victorian England, they don’t “preach what they practice.”  Somehow, this manifests itself in the breakdown of social more at the opposite end of society.

The elites, in Murray’s view, devote their free time to their own obsessions and diversions – exotic foods, chic wines, hybrid cars, and the like – when they should be driving their pickups to Applebee’s to talk about Nascar and the latest episode of “American Idol” with people who barely finished high school.  And somewhere along the way, maybe as everyone is lighting up a cigarette, they’ll slip in a few words about the benefits of a virtuous life.*

I’m sure that Murray, sitting at a table with people who voiced prejudiced, ethnic stereotypes would be quick to remind them that prejudice was not only nasty but economically unwise, since it excludes the capable and virtuous, and that trust, even of those outside our little tribe, is an important source of America’s success.

Several weeks ago, Edward Luce reported in the Financial Times on his lunch with Murray.  Here are some excerpts:  (The full article is here. )

Our venue is Al Tiramisu, a well-hidden Italian restaurant close to Dupont Circle . . . .

He is buoyed when the waiter says the black-truffle pasta is still on the menu, and we both order it as a starter. I have already said he must have a glass of wine. “Now, does the FT extend to a bottle?” Murray asks as he leafs through the wine list.

Our black truffle has arrived. Murray’s martini glass is empty. The waiter pours him a taster from the bottle of Gavi di Gavi, an Italian white wine. “Mmmm, it’s like a good Montrachet,” . . . I ask him what kind of wine a Gavi di Gavi is. Murray discloses that it is a “varietal”. I nod as though I know what that means. It certainly tastes nice. “Varietal means expensive,” he adds.

So much for Applebee’s and a Bud Light.

He discloses that he sometimes plays poker at a casino in Charles Town, West Virginia, and that he will, in fact, head over there after our lunch has finished. “The ways in which it reinvigorates your confidence in America is really interesting,” Murray says.

“I remember sitting at a table a couple of months ago. And at a poker table there’s lots of camaraderie. And so here I am at a typical table at Charles Town. Big guys with lots of tattoos, sleeveless T-shirts, one of them an accountant, the other looks like he comes from a gang. There was an Iranian-American and Afghan-American. Incredible polyglot mix of people – all speak perfect idiomatic English – and the conversation turned to the fact that my daughter was going to marry an Italian. ‘Well, do you trust him?’ they said. ‘You know, you can’t trust those Italians.’”

Murray guffaws at the recollection. “The thing is, it was such an American conversation.”

For what it’s worth, Luce includes the tab:

• Black truffle pasta x2 $90.00
• Sardines $15.00
• Barramundi $28.00
• Gin martini $14.00
• La Scolca Gavi di Gavi $105.00
• Cappuccino $4.50
• Double espresso $7.00
• Total (including tax) $289.50

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* These emblems are taken largely from Murray’s “How Thick Is Your Bubble” quiz in Chapter 4 of Coming Apart.  You can find all 25 items here.