Wednesday, April 19. 2006
Time to see about setting up proper podcasting with my PDA.
Tuesday, December 27. 2005
No, I am not talking about cages, although, I may talk about that in a later entry.
What I am talking about is the Prisoners Dilemma. This is probably the most well known game in Game Theory, a branch of mathematics. Now don't you get that far-away look in your eyes, there is going to be very little math in this entry. If you can subtract 2 single digit numbers, then you'll be fine.
The prisoners dilemma goes like this, You and a friend get caught by the po-lice for doing those crimes. The copper (maybe its Silva, or Gould!) comes to you and says "We know you and your friend did those crimes, so you have to face facts, you are going to Jail. But I am going to give you a deal. If you and your buddy both confess, you'll be in the clink 6 months. If you both proclaim innocence, you both get 3 years. If you say you're innocent, and he admits guilt, then you get off scott free, and he gets 5 years! But the same goes for you, if you admit guilt, and he says he is innocent, then you're packin the fudge for 5 long years. You better have a lot of cigarettes. On, and your buddy is given the same deal." You can't talk to your friend, so you can't work out a reasonable trade. So what would you do?
What you should do depends on what your friend will do. Is your friend going to proclaim innocence? In that case, you should as well. Which means that you both are going to serve 3 years in jail. But then, your friend probably figured that out, so he might admit guilt, hoping that you will too, so its a short 6 month stay. Sweet! But then if he is going to admit guilt, you might as well proclaim innocence, so you can get off scott free! But he surely has thought this through as well, so he will proclaim innocence...
Think it through for a little while, what would you do? Why? What is the most logical and rational choice?
The result is, that there is no "logical and rational" choice. The most logical and rational choice really depend on what the other individual does, and because there isn't any way to know that in advance, there is no rational choice.
Stupid! Stupid! You're so stupid!
The interesting thing happens when you vary the parameters of the game. Instead of it being locked in a prison, say instead it is given a big big cash prize. You and a friend have a choice of sharing the money, or taking it all. If you both share, you both get three million dollars. If one of you takes it all, and the other shares, then the taker gets five million dollars and you get nothing! Stupid! Stuuupid! You're so stupid! If you both try to take it all, then you both get nothing.
Or, lets turn it a little morbid, you and your friend are wired up and strapped to a chair. There are 2 buttons on the arm-rest, one labelled "C" and one labelled "D". If you both press D you both get a severe shock, but stay in the chair. If one of you presses C and the other presses D, then the D player goes free, gets one million dollars, and the C player dies. If you both press C, you both are free to go.
There are all kinds of interesting variations you can do with this game. Douglas Hofstadter has written about this in "Metamagical Themas" (its not a book on magick, rather it is a book on mathematical games) and it is well worth a read. One of the variations he chooses is a game where two players trade bags full of stuff. One bag full of money, and one bag full of sex-toys, music-gear, drugs or some such thing. Would you give the person an empty bag, hoping to get something for nothing? Ohh how sweet! But what if he does the same thing... wouldn't it be best if you both co-operated? But then you'd be the patsy...
All of these variations have great philosophical and even storytelling value, but they can be boiled down to a very simple explanation called a "Payoff Matrix". It looks like this:
|C||3, 3||0, 5|
|D||5, 0||1, 1|
Where "C" is when the player co-operates (admits guilt, puts the money/sex-toys in the bag, whatever) and "D" is when the player defects (claims innocence, leaves an empty bag). The numbers are how many points the players get. Thus if you defect and your friend co-operates, you get 5 points, and he gets none.
Iterated Prisoners Dilemma and other variations.
One very interesting variation on the prisoners dilemma is the Iterated Prisoners Dilemma. Instead of just one single game, the two players play a series of games, and rack up points together. Robert Axelrod explored this in depth, and set up a competition where players would write a program to play a set of prisoners dilemma against each other. There were various strategies employed, and Robert Axelrod added a few extra strategies like "all -co-operate", "all defect" and "random". After pitting all of these programs against each other, what he found was interesting. The winner of the first round was a strategy called "tit-for-tat" programmed by Anatol Rapoport. The program itself is super simple. Start your first move off by co-operating, and then play the previous move of the other player. This means that any time the other player defects, tit-for-tat will punish the other player by defecting once. If the other player gets co-operative at any point however, tit-for-tat will respond in turn with kindness. So when a tit-for-tat meets up with another tit-for-tat, they maximize their return by getting 3 points each round. The same goes with tit-for-tat vs. all-co-operate. When a tit-for-tat meets an all-defect, tit-for-tat looses the first round, and doesn't loose any more.
When Axelrod analyzed the top scoring strategies (of which tit-for-tat was one) he found that all of them had a certain set of properties:
- A winning strategy has to start off by co-operating.
- But just because it starts off nice, doesn't mean it has to continue to be nice. The strategy must also not let other strategies exploit it. (tit-for-tat is retaliatory, but all-co-operate is not)
- A good strategy should be forgiving enough so that the players can get back on a co-operative track, maximizing points.
- The strategy should only be concerned with scoring as many points as it possibly can, rather then scoring more then its opponent.
The iterated prisoners dilemma can be taken further. In 2004 (the 20th anniversary of the first Iterated Prisoners Dilemma competition) a team from Southampton University led by Professor Nicholas Jennings took the lead with a completely different track. Instead of submitting a single program, they submitted 60. The first set of moves played by the strategies was an identification code. If the opposing player played the right sequence of moves, one strategy would co-operate all the time, and the other would defect. Effectively one strategy would take the bullet for another. Any time the strategy met with another strategy that it didn't recognize, it would go all-defect on its ass, thereby minimizing the points that could be gained by the other player. The Southampton strategies took the top three spots, as well as a bunch toward the bottom.
This would suggest that if you are in an iterated prisoners dilemma situation, the best thing you can do is identify with a tribe or collective with a well delineated boundary of slaves willing to take bullets, and kings who get defection-love. Well, its good for the kings of the tribe at any rate.
The prisoners dilemma in daily life
The prisoners dilemma is also applicable to real life. Frequently we are faced with situations where we are given the choice to "cooperate" or "defect". I have a gut instinct against boiling down my human interactions in this way, as if it somehow cheapens the interaction. However, we do this all the time without thinking about it. Whether or not we say that an individual is trustworthy or not depends on how many times that individual has cooperated or defected. Now I don't know if it is a good thing to start doing this, can you imagine keeping a PAD or PDA, with a list of people and their C/D score? On the other hand, we already to that mentally to one degree or another, however our memories are a jumble of vague feelings and recollections of the individuals C/D score, rather then a pure number.
When I apply the prisoners dilemma to my own life, I like to think that I am a Tit-for-Two-Tats kind of player. But then, we all like to think the best of ourselves. I probably defect-first more then I wish to admit to myself. Perhaps keeping track of my own plays in the world-game-of-prisoners-dilemma is like playing a C move, as opposed to the other side of the coin, where I would keep track of everyone elses moves?
What would you do, cooperate? or defect?