April 2, 2008
Tit for Tat: over-rated
In a comment on last week’s Dear Economist, Carl Dahlman wrote:
As Axelrod showed many years ago, the most effective incentive scheme is also the simplest: tit-for-tat. Tit: if you do you chore well, I’ll up the ante by doing mine even better. Tat: if you don’t, I won’t either.
This turns out, surprisingly, not to be true, although it is very widely believed (and Carl’s comment is perfectly sensible). For a trenchant discussion, here is a brief essay from mathematician-turned-economist-turned-political philosopher, Ken Binmore. I find Ken’s style a little harsh, but I can’t argue with the man’s conclusions. Here is an important extract:
The two-state finite automaton TAT-FOR-TIT is the simplest example of the type of mean machine that emerges from Probst’s simulations. This strategy begins by defecting and continues to defect until the opponent also defects. At that point TAT-FOR-TIT switches to its co-operative state. It continues to co-operate until the opponent defects, which behaviour it punishes by returning to the defection state in which it started the game. A player using TAT-FOR-TIT therefore begins by trying to exploit his opponent, and only starts to co-operate if he finds that she is trying to exploit him in the same way that he is trying to exploit her.
The whole thing is slightly technical but well worth a read. Or read an old column of mine, which concludes:
In any case, “tit for tat” is not quite as successful as conventional wisdom would have you believe. A team from Southampton University kicked “tit for tat” off the top spot in a rerun of Axelrod’s tournament by entering a collection of team players who colluded with each other. Another successful strategy is “tat for tit,” which first tries to exploit the other person and plays nicely only if that doesn’t work. Another winning approach is even more depressing, punishing cheats with eternal vengeance.
It is known simply as “grim.”
In his book, Axelrod said quite specifically that Tit-for-tat was NOT always the best strategy to play, he said quite explicitly that a strategy designed to beat tit-for-tat will in fact do so. However, his point was that when you don’t know what strategies your opponent is using, and you know its an ITERATED PD, tit-for-tat does very well. With cooperative types it achieves the highest level of mutual gain, and with mean types (like tat-for-tit) it loses but only by a very small margin in the iteration. When tit-for-tat loses, it doesn’t lose by much. By playing a game like tat-for-tit you can beat tit-for-tat, if only by a tiny margin - but so what, you run the risk of instead playing with someone like “grim” where now you’re stuck in a cycle of defections.
Axelrod’s point was that in a world of MANY STRATEGIES - tit-for-tat will become dominant. Though yes, he expands on this by taking account of noise and misinterpreted signals in his second book, so its more complicated than that, but the foundation is still tit-for-tat when all is said and done.
Posted by: Max | April 3rd, 2008 at 9:50 pm | Report this commentThe Southampton gambit was very clever, but it doesn’t really say anything important about the evolution of strategies. Southampton took advantage of a loophole in the tournament rules that allowed them to submit as many “ringer” strategies as they wanted. The Southampton team entered a bunch of “slave” strategies that would submit to their “master” strategies. The problem is that, in a real evolutionary environment, the poorly performing slave strategies would fail to reproduce — and therefore the masters would be deprived of their slaves. More here: http://agoraphilia.blogspot.com/2004/10/rumors-of-tit-for-tats-death-greatly.html
Posted by: Glen | April 3rd, 2008 at 11:42 pm | Report this commentTim
Posted by: NBeale | April 5th, 2008 at 11:33 pm | Report this commentA modern treatment of this is in Nowak’s brilliant book “Evolutionary Dynamics” which shows amongst other things how Generous Tit for Tat and Win-Stay-Lose-Shift can dominate Tit-for-Tat.