Chimps beat humans at game theory

In Chimpanzee choice rates in competitive games match equilibrium game theory predictions, a paper in Nature by Colin Camerer and colleagues, researchers document the astounding performance of chimpanzees in classic game-theory experiments -- a performance that's substantially superior to humans who play the same games: Read the rest

On anachronism in literary analysis

Jane Austen was not a game theorist. Read the rest

Strategies for the future: accuracy vs. resilience vs. denial

Seth Godin's daily thoughts are always provocative and thoughtful, but today's is a particularly timely and apt one for the new year. Godin describes three ways of coping with the future: Accuracy (correctly guessing what will happen); Resilience (admitting you can't make accurate predictions, so preparing to weather a variety of storms); and "Denial" (pretending nothing will change and getting clobbered as a result). I'm shooting for "Resilient" myself, but if I'm brutally honest, I have to admit that I have moments where I assume that I can be Accurate and where I'm too tired to do anything except Deny. Read the rest

Betrayers' Banquet: gourmet dining vs the Prisoner's Dilemma

Ed writes, "The Betrayers' Banquet is an experimental dining experience from London, where guests play the iterated prisoner's dilemma to win a better or worse meal. Each of the 48 participants is served eight different courses over two hours; two starters, four mains and two desserts. While all dishes are edible, their allure differs considerably between the top and the bottom of the table; those at the top will enjoy a fine dining experience to match any in London, while those at the bottom will grapple with pickled walnuts, chicken's feet soup, lumpy gruel, and worse." Read the rest

Twitter party game/Prisoners' Dilemma: "I Eat Poo"

Jeremy Bornstein proposes a party game/Prisoners' Dilemma variant called "I Eat Poo," in which the players pass their phones to their left and invite the player there to type (but not send) an embarrassing message into their own Twitter account. Phones are handed back and each player gets to decide whether to allow the message to be posted, or to forfeit $20 to the message-writer; the phones are handed back to the message-writer, and the hand-over may also include a covert $20 payoff. The climax comes when the final accounting is made: if everyone has paid $20, or no one has paid $20, then nothing happens (the messages aren't posted). Otherwise, the paid-up don't get posted, the unpaid do, and the pot is split among the message-writers. Read the rest

What happens when actual prisoners play The Prisoner's Dilemma?


The Prisoner's Dilemma is a basic part of game theory. Two prisoners are given the choice between informing on the other, or staying silent. They can't communicate with each other. The choices they make determine how many years in prison they both get.

This analogy/brain game is often used to demonstrate the ways that different people can work with or against each other in economic and social situations. Now, for the first time, scientists have done a study based on The Prisoner's Dilemma that used real prisoners. Instead of time off their sentences, they were given the choice of competing or cooperating to earn goodies like coffee and cigarettes.

And here's the surprise: Compared to college students, the prisoners actually cooperated with each other much more often. Read the rest

Tic-Tac-Toe squared

Want to play a game of Tic-Tac-Toe that's genuinely challenging and hard? Try "Ultimate Tic-Tac-Toe," in which each square is made up of another, smaller Tic-Tac-Toe board, and to win the square you have to win its mini-game. Ben Orlin says he discovered the game on a mathematicians' picnic, and he explains a wrinkle on the rules:

You don’t get to pick which of the nine boards to play on. That’s determined by your opponent’s previous move. Whichever square he picks, that’s the board you must play in next. (And whichever square you pick will determine which board he plays on next.)...

This lends the game a strategic element. You can’t just focus on the little board. You’ve got to consider where your move will send your opponent, and where his next move will send you, and so on.

The resulting scenarios look bizarre. Players seem to move randomly, missing easy two- and three-in-a-rows. But there’s a method to the madness – they’re thinking ahead to future moves, wary of setting up their opponent on prime real estate. It is, in short, vastly more interesting than regular tic-tac-toe.

Ultimate Tic-Tac-Toe (via Kottke) Read the rest

Stag Hunts: fascinating and useful game theory model for collective action problems

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) Read the rest

Using Silk Road: game theory, economics, dope and anonymity

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) Read the rest

Students get class-wide As by boycotting test, solving Prisoner's Dilemma

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.

Read the rest

High-stakes one-shot Prisoner's Dilemma on a British game show with an astounding strategy

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" Read the rest

What is a game?

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.

Read the rest