Dinhternet

It’s not a ques­tion I ask often, but it crossed my mind the other day in my ECN 122 class as we were talk­ing about The Pris­on­ers’ Dilemma. For any­one not famil­iar with it, The Pris­on­ers’ Dilemma is a clas­sic game the­ory sce­nario that goes some­thing like this:

Two sus­pects are brought in by the police because they are believed to be involved in a major crime. The police have enough evi­dence to con­vict them of a minor crime, but not enough to con­vict them for the major crime. The two sus­pects are held in sep­a­rate cells and can­not com­mu­ni­cate with each other. When each pris­oner is ques­tioned, he is told that he will be spend­ing a year in prison for the minor crime. How­ever, if he con­fesses that he and other sus­pect com­mit­ted the major crime, the police will set him free and imprison his friend for twenty years. And if both pris­on­ers con­fess, then they will both spend six­teen years in prison.

If you were in this sit­u­a­tion, what would you do? It’s a very inter­est­ing case, from a game the­ory per­spec­tive. (You might have a dif­fer­ent opin­ion of it if you were tak­ing the ACLU’s perspective.)

In game the­ory, The Pris­on­ers’ Dilemma is an exam­ple of a finite strate­gic game, which means that there’s a finite num­ber of play­ers, a finite num­ber of actions avail­able to each player, and a pref­er­ence pro­file on the out­comes for each player. In this case, there’s two play­ers, and they each have two actions avail­able — con­fess or not confess.

Assum­ing that the play­ers do not enjoy prison, they will pre­fer no prison time to one year in prison to six­teen years in prison to twenty years in prison. That means that they want to con­fess and have the other sus­pect not con­fess. But fail­ing that, they would would nei­ther to con­fess. Or at least both con­fess. But the worst pos­si­ble out­come is to not con­fess and have the other sus­pect confess.

So in game the­ory, you’re sup­posed to look for a dom­i­nant action, or an action which gives you the best pos­si­ble out­come no mat­ter what the other player(s) do. In this case, the dom­i­nant action is to con­fess. If the other player doesn’t con­fess, con­fess­ing gives you a bet­ter out­come — going free ver­sus a year in prison. If the other player does con­fess, con­fess­ing still gives you a bet­ter out­come — six­teen years in prison ver­sus twenty years. But if both play­ers play the dom­i­nant action, they would both get six­teen years… much worse than if they had just both coop­er­ated and got­ten one year each.

So… know­ing all that, what would you do? When we played in class, David Y and I were paired up, and we both chose to not con­fess. It takes a cer­tain amount of trust to do that, though. David Y said that if he was just paired up with some stranger in class, he def­i­nitely would have confessed.

So yes­ter­day, after that post about my stut­ter­ing psych pro­fes­sor, I went to my econ class. I knew Albert was going to be there, but I didn’t know David Y would be there too. But the best sur­prise was this: my econ pro­fes­sor also stut­ters. And on top of that, he has a Ger­man accent. In fact, I would say he’s quite new to Amer­ica, because he sched­uled a midterm on the day of Thanksgiving.

It wasn’t so bad, though. Unlike my first pro­fes­sor, I think this one was just stut­ter­ing because he was ner­vous, and he stopped halfway through lec­ture. Also, since the class is about game the­ory, we got to play some inter­est­ing games the first day. In fact, he put his own money on the line for a game to make it more inter­est­ing for us.

Here’s the rules: every­one writes down a num­ber between 0 and 100 on a piece of paper and turns it in. The per­son who is clos­est to two-thirds of the aver­age of the num­bers wins! The pro­fes­sor used that as a weeder, and then played heads-up against the class win­ner of that round for $5 of his own money. (The stu­dent put noth­ing on the line.)

What num­bers would you pick in that sce­nario? (Keep in mind that you do not know the other play­ers at all, and you prob­a­bly can’t guess what they will pick with any sort of accu­racy, unless you are a con man with an uncanny abil­ity to cold read peo­ple.) Would you pick the same num­bers for both rounds?

Open the spoiler sec­tion to see the strat­egy behind the game.
Show ▼

It’s a bit toasty in here, so I’m gonna try to make this as fast as possible…

Wednes­day… woke up and went online, of course. Chat­ted with Peggy, although I shouldn’t have, because I was dis­tract­ing her from study­ing again. Read more of Crypto­nom­i­con.

Went over to Kitty’s for lunch. I needed to bor­row their microwave to heat up some left­overs. Ended up stay­ing there and watch­ing the first half of Man of the House. It was bet­ter than I expected. Although that’s not say­ing much.

Then it was time for the BBBS Team Ten­nis project. I picked up Thu H, Eric, Ali­son, and David Y, and we were off. Good thing I decided to leave Davis so early, because traf­fic was pretty bad, and we just made it on time.

Dur­ing the drive there, I started break­ing out in hives again, so dur­ing the whole project, I was fight­ing the urge to scratch myself. It was really hard. Mommy Van had to slap me a few times. There were times when I wanted to just leave the project. I might have actu­ally done it if I wouldn’t be strand­ing four peo­ple in Cit­rus Heights. It wasn’t so bad when we were busy, though… con­stantly pour­ing beers kept my hands busy and off myself.

Some of the taps (the MGD in par­tic­u­lar) were finicky, though, so David and I had some prob­lems pour­ing at first. Even­tu­ally, we filled up and actu­ally over­flowed the drain bucket under the taps. (It’s a five gal­lon bucket!) Quote comes from that…

Notice how he didn’t actu­ally call it beer. And then we kept dar­ing each other to drink the bucket. Mmm… five unsan­i­tary gal­lons of warm mixed beers. Or, as I called it, the ulti­mate King’s Cup.

Rhonda left the project early because she had bron­chi­tis, and it was a bit unor­ga­nized. Angela did the best she could, though. The big prob­lem was shut­ting down at the end. None of the BBBS peo­ple seemed to really know how it was sup­posed to go down. It took them for­ever to count the money.

And then there was the prob­lem with the wine. It was entirely my fault for not tak­ing care of things on the spot, but I was so pre­oc­cu­pied with try­ing not to scratch myself I didn’t. I took my car home early. Well, we actu­ally left the project at 11, and I didn’t get home until 12. Oh, and Thu H was so con­cerned about the hives, she kept try­ing to make me take med­i­cine, and when I insisted it would go away in time, she called up a bunch of peo­ple to con­vince me oth­er­wise, includ­ing Clint. Before I dropped her off, she demanded we go to Safe­way, where she bought a tube of anti-itch cream for me, too. When I got back to my apart­ment, I took a long cold shower and most of the hives went away, so I didn’t use the cream.

Called up Peggy, and she came over to watch movies. She insisted on watch­ing Evil Dead and Evil Dead 2 so Drew can’t make fun of her any­more. (She’d already seen Army of Dark­ness, or we’d have watched that, too.) The hives moved down to below the waist, but I was well dis­tracted.

After the movies, Peggy went home, and I passed out.