Wednesday, October 13, 2004

Self-Interest and Game Theory

Those interested in game-theory and the like will find this article interesting...

For twenty years, the strategy of Tit for Tat has won the competition. This was the basic strategy employed during the cold war. If you neighbor was nice to you, you were nice to them. If they 'wronged' you, then you answered back with an equal amount of aggression.

It now appears that Tit for Tat no longer works, as long as you have enough 'suckers' in the mix. The new program seeks to recognize 'friendies' playing the game (based on how they act in the first few rounds), then one program goes into master mode, and the other goes into slave mode. The 'slaves' end up at the bottom of the heap, because they are always sacrificing themselves for the 'masters'. The masters end up on top.

4 comments:

David said...

Are you interested in everything I am?

Wouldn't rule out Tit-for-Tat just yet. The tournament is played round-robin with every strategy playing every other strategy, and scores recorded at the end of each game and totalled at the end of the tournament. The Southampton strategies didn't beat Tit-for-Tat head to head - a few of them simply managed to tally more total points over the length of the contest. I don't think we should be surprised by this outcome. Generally, when a team competes against an individual the team wins. That's what happened here, because the rules don't outlaw team play (although personally I think it violates the spirit and the history of the competition).

I think game theory should be an integral part of the work we do - see http://www.reusability.org/blogs/david/ssao.html for notes from a talk I gave that include one way game theory applies to informal online learning communities.

=)

Matthew Buckley said...

Thank you for the links. Yes, this interest goes clear back to my Polisci days, and of course if you like video games you have to think about game theory every once in a while. I've also played around with the prisoner's dilemma thing in my Weber State class and have found a few interesting things. I'm planning on posting that next week when we discuss the whole 'trust' issue.

Anonymous said...

I would say that the Southampton strategy is not very applicable as regards the 'real world'. Any actual organism or organization in a real-world ecological or economic system has to get SOME kind of minimal benefit for itself, simply to survive. An organism or organization which manages to acheive such minimal success will endure. Those which acheive a higher rate of success will spread, either genetically, by having offspring, or through 'memes' as other organisms or organizations voluntarily adopt the successful behavior. Organisms or organizations which 'sacrifice' themselves are not able to do so indefinitely, such as the Southampton slave programs. Sooner or later they fail in some fashion, such as dying of starvation or going bankrupt. After that, the 'masters' will die as well.

Anonymous said...

To go on, I think that a new rule, reflecting real world conditions ought to be added to the gaming tournaments. After every game of 200 (or however many) rounds against an opponent, the AVERAGE score for all those rounds should be calculated (which could be anywhere between 0 and 3), and depending on the score, one of the following should be done:

Average < .75: Program fails to 'survive', is removed immediately from the tounament

Average from .75 - 1.5: Program manages to 'survive', goes on to next round

Average from 1.5 - 2.25: Program survives and also makes one additional copy of itself which is entered into the next round.

Average> > 2.25: Program survives and makes 2 copies of itself which are both entered into the next round.

After many rounds have been played, it should be interesting to see not only which programs have the highest score, but which have reproduced the most times. I am betting on 'tit for tat', which although will only have one 'reproduction' when playing itself, and none when playing Southhampton, will nevertheless always survive and in the long run I think do much better than Southampton, because the double reproduction of the 'masters' will not last long once all the slaves have been removed from the game.