More on TIT-FOR-TAT
Hoisted from Comments for Further Discussion: TIT-FOR-TAT...
I wrote what I thought was an innocuous:
Tom Slee Tells Us That Game Theorist Anatol Rapoport Has Died: Rapoport's "Tit-for-Tat" solution to repeated prisoner's dilemma has two huge things going for it:
- You cannot exploit it. You are always better off cooperating than attempting to game it. It's simple, so it's easy to figure out what it is and what it is doing.
- These are two very powerful advantages in any strategic interaction.
Crooked Timber: Anatol Rapoport... perhaps... most widely-known... the Tit-for-Tat rule for repeated games of the Prisoner's Dilemma, embodied in a four-line program Rapoport successfully entered in a contest run by Robert Axelrod. Rapoport's program co-operates inititially, and thereafter matches the other player's last action, defecting in response to a defection, and returning to co-operation if the other player does so...
And produced a bunch of comments:
[Simplicity and non-exploitation] can be said for many other strategies, including cooperating until the other player defects and then defecting in perpetuity. It adds nothing to the literature on credibility in decision-making save a convenient reference. Kenneth Arrow's work is non-obvious and counterintuitive. Much of the rest [of game theory] is formulaic rationalization built on questionable axioms which drive to logical conclusions assuming one buys into those axioms. It may be a bit much holding Rappaport responsible for what game theory has become. May he rest in peace.
I don't quite understand the comment. It's true, of course, that there are other strategies that meet those two stated conditions; but (and perhaps this ought to have been stressed along with them) it was Rapoport's that won the contest against all the clever complexities that were submitted. Its ability to run up a higher score against a variety of strategies under more or less realistic conditions than "defect in perpetuity" seems fairly clear a priori. Again, is there a reference for "holding Rappaport responsible for what game theory has become"? It's not clear that Tom Slee is making such a strong claim; nor whether that's supposed to be a good thing or a bad one. Certainly AR was a leader of opposition to what the Rand Corporation was turning game theory into, and he seems to have been influential in that effort; and it's hard to see that as any but a good thing.
It certainly seems to describe historical reality pretty well... "...two agents playing tit for tat remain vulnerable. A one-time, single-bit error in either player's interpretation of events [e.g.Iraq] can lead to an unending 'death spiral'. In this symmetric situation, each side perceives itself as preferring to cooperate, if only the other side would. But each is forced by the strategy into repeatedly punishing an opponent who continues to attack despite being punished in every game cycle. Both sides come to think of themselves as innocent and acting in self-defense, and their opponent as either evil or too stupid to learn to cooperate" http://en.wikipedia.org/wiki/Tit_for_tat#Problems. i.e. the armchair general types hunkered down in front of their TV sets and war blogs, with buckets of popcorn, drawn into the Iraq War like the complicated plot of a fiendishly violent soap opera, feverish imaginations convinced that that the only option is to keep playing, playing, and playing, double or nothing, until Norman Podoretz's World War 4 egg is finally hatched and the corpses pile high.
In econ and ev psych Gintis and others have supplemmented simple reciprocity (approximately tit for tat) with strong recoprocity (altruistic retaliation against defectors, even at personal cost for the retaliator). Individualist simple reciprocity can't deal with a crippling first strike. Strong reciprocity usually works within a defined community, all members of which are committed to backing up the others.) "Moral sentiments and Material Interests", Herbert Gintis, Samuel Bowles, Robert Boyd, and Ernst Fehr, eds., MIT, 2005.
Walktheline's comment was the first I've ever seen making counterintuitivity a necessary requirement of good work, though economists and the like often seem to behave as though it were. The dadaists of science...
The claims made by Axelrod in favor of tit-for-tat are wildly overblown, and frequently just plain wrong. Anatol Rapoport cannot really be blamed for his sloppiness, although he did (re)invent the Symmetry Fallacy that purports to demonstrate that it is rational to co-operate in the one-shot Prisoners' Dilemma. A good place to read a game theorist's reaction to all of this is in Ken Binmore's "Playing Fair: Game Theory and the Social Contract I," Chapter 3, (MIT Press, 1994).
Jesus, this guy has enemies.
I've seen very, very unpleasant things written about Rapoport's intro to the Penguin edition of Clausewitz, though whether those comments illuminated R. or his critics I could not say.
It's not clear what Brad DeLong means by 'Rapoport's "Tit-for-Tat" solution to repeated prisoner's dilemma.' Tit-for Tat is neither evolutionarily stable nor subgame perfect in the infinitely repeated Prisoners' Dilemma, so not really a "solution" at all. In fact no strategy is evolutionarily stable in this game, but there are many subgame perfect strategies, including the Grim Strategy, which punishes by reverting to Confess forever after the first deviation from cooperation. Anatol Rapoport was a great man in many ways, and a pioneer of applied game theory, but the confused acclaim accorded to his tit-for-tat strategy probably does him little justice.
Porlock -- I may have been unfair to Rapaport. I'm just underwhelmed by the inference that mathematically formalizing tit-for-tat behavior is an intellectual accomplishment. John Emerson -- I understand your point. In my defense, I just don't see the point in embracing game theoretical models unless they teach us something new. The novelty of most such papers I've read lies in the implicit claim they make about social rationality through their use of models that quantify utility. There are major problems with this, not the least of which is that it is rarely clarified whether the models presented are intended to be descriptivist (attempts to explain actor behavior) or prescriptivist (strategies to maximize utility). Note the way comments two and three on this thread assume different things here. Anyway, I consider it incredibly misleading (a major step backwards) for scholars to embrace a form of argument that permits form to obfuscate what is really under discussion. Working through something like Arrow's theorum is a reminder of the validity and worth of the approach though, because Arrow avoids these traps and teaches us something we don't already know. So I 'm not willing to dismiss the approach, but I don't get anything close to that from reading Rapaport or Axelrod or the other IR game theorists.
Let me just re-comment on two:
Tit-for Tat is neither evolutionarily stable nor subgame perfect in the infinitely repeated Prisoners' Dilemma, so not really a "solution" at all. In fact no strategy is evolutionarily stable in this game, but there are many subgame perfect strategies, including the Grim Strategy, which punishes by reverting to Confess forever after the first deviation from cooperation...
Anatol Rapoport cannot really be blamed for his sloppiness, although he did (re)invent the Symmetry Fallacy that purports to demonstrate that it is rational to co-operate in the one-shot Prisoners' Dilemma...
The fact that GRIM is subgame-perfect suggests a problem with subgame-perfection as one's equilibrium concept, no?
And the Symmetry Argument is not the Symmetry Fallacy. It's remarkably deep and subtle, raising many of the issues that arise in Newcomb's Problem. Let me see if... No, this would take too long. More later...