Yesterday, I wrote about some Johns Hopkins students who overcame a game theory problem and got an A for the whole class. I called it a non-iterated Prisoner's Dilemma, but as Tim Harford points out, it's more of a Stag Hunt, a game theory category that I hadn't been aware of, and which has fascinating implications for lots of domains, including Internet peering:

In the stag hunt, two hunters must each decide whether to hunt the stag together or hunt rabbits alone. Half a stag is better than a brace of rabbits, but the stag will only be brought down with a combined effort. Rabbits, on the other hand, can be hunted by an individual without any trouble.

There are two rational outcomes to the stag hunt: either both hunters hunt the stag as a team, or each hunts rabbits by himself. Each would prefer to co-operate in hunting the stag, but if the other player’s motives or actions are uncertain, the rabbit hunt is a risk-free alternative.

Right on queue

(Image: [ C ] Lucas Cranach - Stag Hunt of the Elector John Frederick, a Creative Commons Attribution (2.0) image from centralasian's photostream)

Gwern's "Using Silk Road" is a riveting, fantastically detailed account of the theory and practice of Silk Road, a Tor-anonymized drugs-and-other-stuff marketplace where transactions are generally conducted with BitCoins. Gwern explains in clear language how the service solves many of the collective action problems inherent to running illicit marketplaces without exposing the buyers and sellers to legal repercussions and simultaneously minimizing ripoffs from either side. It's a tale of remix-servers, escrows, economics, and rational risk calculus -- and dope.

But as any kidnapper knows, you can communicate your demands easily enough, but how do you drop off the victim and grab the suitcase of cash without being nabbed? This has been a severe security problem forever. And bitcoins go a long way towards resolving it. So the additional security from use of Bitcoin is nontrivial. As it happened, I already had some bitcoins. (Typically, one buys bitcoins on an exchange like Mt.Gox; the era of easy profitable "mining" passed long ago.) Tor was a little more tricky, but on my Debian system, it required simply following the official install guide: apt-get install the Tor and Polipo programs, stick in the proper config file, and then install the Torbutton. Alternately, one could use the Tor browser bundle which packages up the Tor daemon, proxy, and a web browser all configured to work together; I’ve never used it but I have heard it is convenient. (I also usually set my Tor installation to be a Tor server as well - this gives me both more anonymity, speeds up my connections since the first hop/connection is unnecessary, and helps the Tor network & community by donating bandwidth.)

Using Silk Road (via O'Reilly Radar)

Johns Hopkins computer science prof Peter Fröhlich grades his students' tests on a curve -- the top-scoring student gets an A, and the rest of the students are graded relative to that brainiac. But last term, his students came up with an ingenious, cooperative solution to this system: they all boycotted the test, meaning that they all scored zero, and that zero was the top score, and so they all got As. The prof was surprisingly cool about it:

Fröhlich took a surprisingly philosophical view of his students' machinations, crediting their collaborative spirit. "The students learned that by coming together, they can achieve something that individually they could never have done," he said via e-mail. “At a school that is known (perhaps unjustly) for competitiveness I didn't expect that reaching such an agreement was possible.”

The story of the boycott is a sterling example of how computer networks solve collective action problems -- the students solved a prisoner's dilemma in a mutually optimal way without having to iterate, which is impressive:

“The students refused to come into the room and take the exam, so we sat there for a while: me on the inside, they on the outside,” Fröhlich said. “After about 20-30 minutes I would give up.... Then we all left.” The students waited outside the rooms to make sure that others honored the boycott, and were poised to go in if someone had. No one did, though.

Andrew Kelly, a student in Fröhlich’s Introduction to Programming class who was one of the boycott’s key organizers, explained the logic of the students' decision via e-mail: "Handing out 0's to your classmates will not improve your performance in this course," Kelly said.

"So if you can walk in with 100 percent confidence of answering every question correctly, then your payoff would be the same for either decision. Just consider the impact on your other exam performances if you studied for [the final] at the level required to guarantee yourself 100. Otherwise, it's best to work with your colleagues to ensure a 100 for all and a very pleasant start to the holidays."

Fröhlich's changed the grading system -- but he's also now offering the students a final project instead of a final exam, should they choose.

Dangerous Curves [Zack Budryk/Inside Higher Ed]

A British game-show called "Golden Balls" concludes each installment with a single-shot version of the Prisoner's Dilemma in which the two players' choices can result in a large cash prize being awarded to both of them, neither of them, or just one of them. The players are allowed to tell each other what they plan on doing, but they are also allowed to lie and try to trick the other player into making a choice that would leave the whole pot in the trickster's hands.

In this remarkable clip, a player named Nick runs an extraordinary end-game that has to be seen to be believed. As Bruce Schneier says,

This is the weirdest, most surreal round of "Split or Steal" I have ever seen. The more I think about the psychology of it, the more interesting it is. I'll save my comments for the comments, because I want you to watch it before I say more. Really.

Once you've watched the clip, check out Bruce's spoiler-y discussion of what is going on there.

Amazing Round of "Split or Steal"

Back from the Games Developers' Conference in San Francisco, Raph Koster weighs in on the perennial debate about what makes a game, starting with his own classic formulation, "Playing a game is the act of solving statistically varied challenge situations presented by an opponent who may or may not be algorithmic within a framework that is a defined systemic model."

Some see this as a “fundamentalist” approach to the definition. But I use it precisely because it is inclusive. It admits of me turning a toy into a game by imposing my own challenge on it (such as a ball being a toy, but trying to catch it after bouncing it against the wall becoming a game with simple rules that I myself define). It admits of sports. It admits of those who turn interpersonal relationships, or the stock market, or anything else, into “a game.”

Basically, I see this whole issue as this Venn diagram. I group sports, boardgames, and yes, videogames under “game” because all of them are susceptible to being broken down and analyzed with game grammar. They all have rules. They all have an “opponent” that presents varied challenges to the player. They all have a feedback loop. They all present verbs to the player. They all present goals. The fact that some use real-world physics as the opponent, some use the human body, some use dice or boards, and some use a computer is not even relevant when you break down the game atoms. I can group these easily because I’ve dug into them so much that I know there is something there in common.

“X” isn’t a game!