October 25, 2005

I want those who get to know me to become admirers or my enemies

Explaining the Prisoner's Dilemma in class tonight, one of the students said it was like "Friend or Foe." Oh, the Adam Ant song, I said. Complete blank looks--and these are graduate (accounting, mostly) students. But they still might not have been alive in 1982.

Anyway, it seems to have been an MTV game show hosted by Kennedy; as the student explained, at the end of the game each member of the winning team must say "friend" or "foe." If both say "friend," they split the money equally; if one says "foe," he gets all the money; if both say "foe," neither get any money. This isn't quite the Prisoner's Dilemma, because "friend" is only weakly dominant; if the other person says "foe," then it doesn't matter whether you say "friend" or "foe." (Though you might choose to say "foe" just so as not to be a sucker.)

In this game, Foe/Foe is the unique Nash equilibrium; if player A's strategy is Friend with probability p, then for player B to play Foe gives an expected value gain of p*(half the winnings) over saying Friend. The interesting thing, perhaps, is that the Nash equilibrium here actually guarantees that both players get the worst possible outcome. But I've always suspected that Nash equilibria aren't particularly definitive of rationality. (This is the TAR thread referenced therein.) [This paragraph seems to be totally wrong; see comments.]

It would be interesting to know what people actually did when it came to choosing "Friend or Foe." But, alas, not interesting enough for me to put up with Kennedy. People who don't share my allergies are invited to report the results. [UPDATE: Wow, someone already did. Thanks, Joe O. If I'm reading the acknowledgments correctly, it helps to have a teenage daughter.]

Posted by Matt Weiner at October 25, 2005 11:50 PM

Aren't Friend/Foe and Foe/Friend also Nash equilibria in this game?

Posted by: Anders Weinstein at October 26, 2005 12:23 PM

Social Learning and Coordination in High-Stakes Games: Evidence from Friend or Foe

1.Contestants pick "friend" about half the time.
2.This does not depend on the amount of money at risk as previous researchers had suggested.
3.People who anticipate that their oponent will pick "friend" tend to pick "friend", while people who anticipate that their oponnent will pick "foe" tend to pick "foe".
4. People who don't contribute as much to the creation of the pot tend to pick "friend" more often.

Posted by: joe o at October 26, 2005 02:29 PM

Thanks for the tremendously helpful comments!

Posted by: Matt Weiner at October 26, 2005 06:25 PM

I'm pretty sure Kennedy's involvement with the show post-dates the end of her involvement with MTV.

Also, prior to the part where each person chooses whether they are going to go friend or foe, they each get an opportunity to persuade their partner. During this portion, everyone claims they'll choose friend and talks about how loyal and honest they are. After watching for some weeks, my co-watchers and I became convinced that this is a mistake. When operating under conditions of uncertainty, contestants are tempted by the possibility of getting 100% of the prize. If instead you make no attempt to persuade and declare a) that you're going to say foe and b) you'll return a significant portion of the money (49% or slightly less) to your partner afterwards, they at least know that 100% is not in their range of options, and can make their choice with more certainty about the effect of their decision. The problem with this strategy is that there is no way to make b) credible. Also, spite. Nevertheless, it would be such a change of pace from the standard declarations of loyalty that it might just work.

Posted by: washerdreyer at October 27, 2005 12:40 AM

Corrected, but I'm going to stand by irritating--that don't wash off.

I think spite could be very strong your strategy--the Cristina Bicchieri talks at the Formal Epistemology Workshop this year suggested that there's a strong impulse to take people down if you perceive them to be acting unfairly, even if you hurt yourself in the process. One of the games involved was one in which one person gets to split $10 between himself and another, and the other gets to accept the offer or refuse it (in which cases both get nothing). Pure maximization predicts that I give you as little as possible, and you take it, but in practice people split more evenly and if they pushed their luck the offer was sometimes refused.

And if it was presented as a situation where the chooser earned it--if, for instance, they were told that the chooser had scored higher on a test--then the chooser tended to take more money, and the other player tended to accept it. Compare Joe's #4.

So if I say, "I'm going to say 'foe', and then I'll give you less than half the money," the spite factor could be very powerful. Add to that, if each player can trust the other to honor the agreement about the money, they can agree to both say 'friend'--it doesn't matter who gets the money initially. Although maybe the "I'll take a little extra" gives the other person more reason to believe that you actually intend to carry the plan out.

Posted by: Matt Weiner at October 27, 2005 10:35 AM

Keep your philosophy.

Posted by: Matt's mom at October 27, 2005 01:21 PM

That is, keep your philosophy, wa wa hey.

Posted by: Matt's mom at October 27, 2005 01:26 PM

pwned by my own mother! (Google the title of this post, if you need a crib sheet.)

Posted by: Matt Weiner at October 27, 2005 06:03 PM

You know, I'm a grad student, and I was alive for only five sixths of 1982.

Posted by: ben wolfson at October 31, 2005 07:27 PM