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A Prisoner's Dilemma

 
 
rufio
 
Reply Mon 28 Feb, 2005 07:27 pm
Do most people here know about this game? (If you do, you can skip the next paragraph.)

Basically, you have two people playing each other, and the objective is to get as many points as possible (but not necessarily more points than the other person, if I understand right). Each person can choose either to cooperate or defect, and they can't see what the other one chose before making their choice. If both cooperate, than they both get 3 points. If they both defect, than they both get 1 point. If one cooperates, and the other defects, than the defector gets 5 points and the cooperator gets none.

Anyway, strategies for this are generally not geared towards beating or penalizing the other person, but towards getting the most points for yourself (that is, to cooperate). My compsci prof built a program which took a number of simple AI personalities and paired them off in a round-robin sort of a deal and had them play a tournament, to see who wound up with the most points. Each personality utilized a different strategy. He started with:

1. Just Mean: Defects every round.
2. Look Back: Responds with the other player's last move.
3. Absentee: Cooperates for the first two rounds, and thereafter defects only if its opponent defects twice in a row.
4. Pavlov: Cooperates the first round, and then cooperates if it and its opponent chose the same option in the previous round, and defects if they chose differently.
5. Gotcha: Does the same thing as Look Back, only defects for no apparent reason in turns 40 and 60.
6. Tester: Defects in the first round, cooperates in the second round, and continues to switch until the other player defects - than it does the same thing as Look Back.
7. Friedman: Cooperates until the other player defects, and then defects every subsequent round.
8. Punisher: Cooperates, until the other player defects. The first time that happens, it defects in the next round only; the second time it defects for the next two rounds, and so on.
9. Forgiver: Begins by cooperating, then keeps track of two totals: a) how many times the other player has defected in response to Forgiver cooperating in the previous round, and b) how many times the other player has cooperated since last defecting in that way. If a is more than one greater than b, Forgiver defects; otherwise, it cooperates.

Anyway, I've got the program on my computer, and I've run it and seen the results of the tournament. I thought it would be fun if I posted it here, and people could try and guess who would win.

I also wrote a few strategies myself, if anyone wants to see those in action - and if someone thinks they have a better strategy, I can code it and run that in the tournament too. Very Happy

Edit: Forgot Friedman. Whoops.
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Type: Discussion • Score: 2 • Views: 1,012 • Replies: 7
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rufio
 
  1  
Reply Tue 1 Mar, 2005 01:56 pm
Does this interest no one?
0 Replies
 
joefromchicago
 
  1  
Reply Tue 1 Mar, 2005 04:22 pm
rufio: Most of these strategies have been utilized before in iterated prisoner's dilemma (IPD) games. Your professor's "Pavlov" strategy sounds like the "tit for tat" strategy that Robert Axelrod identified as the optimal strategy for IPD games. For those interested in a brief explanation of this strategy, click here.

It should be noted that most IPD games do not have a set ending point: otherwise, they might be subject to a backward induction paradox.
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justwork
 
  1  
Reply Tue 1 Mar, 2005 05:06 pm
I think its a pretty cool idea. Who ended up winning?
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rufio
 
  1  
Reply Sat 5 Mar, 2005 07:57 pm
Eeech, I need to come back here more often. Joe, the assignment was based on the Axelrod experiment - I think those are the original players in it, actually, which he provided source code for. (Pavlov doesn't do great, though - Look Back wins.) Anyway, we ran our own version of it with players written by the class, which is here:
http://www.cs.grinnell.edu/~stone/courses/scheme/labs/prisoners-dilemma-report.xhtml

He's also got a link to the source code of all of our players, if you can read Scheme. I'm responsible for Pragmatist and Vizzini (although Vizzini wasn't intended to do well, so....). Guesser was sort of a early bastard version of Pragmatist, because I suck at lists.
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psychonerd
 
  1  
Reply Sun 6 Mar, 2005 10:33 pm
The winning strategy depends on:
1) how many rounds you have, and
2) how many of the "players" are "nice", and how many are "mean".

If I remember correctly, that is.

Keep posting on the subject, it's an interesting one!
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joefromchicago
 
  1  
Reply Mon 7 Mar, 2005 10:09 am
rufio: You go to Grinnell? One of my best friends went there. I visited the campus on a couple of occasions. Good school, but stuck in the middle of nowhere.
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rufio
 
  1  
Reply Mon 7 Mar, 2005 03:50 pm
Psychonerd - yeah it depends a lot on the other players. In theory, the number of rounds is randomly chosen, and no one knows what they are ahead of time. There was also something in there about being "retaliatory" and "forgiving" that was supposed to work well. Pragmatist seemed to do well regardless (especially when Vizzini played) but still didn't beat Look Back in the original line-up. Hmmm.

Joe, yeah I go to Grinnell. I thought it wasn't that well-known, but for some reason I keep turning around and meeting people who know someone who went there. The smallness and the middle-of-nowhereness was part of why I wanted to go. I'm not really a big fan of big cities. It's nice to be able to leave your car unlocked, and take walks by yourself at 2 AM, and have people who don't know you greet you in passing. Man, I'm really boring, aren't I?
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