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:

1. You cannot exploit it. You are always better off cooperating than attempting to game it.
2. 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 has died at the age of 95. Among many contributions, perhaps his most widely-known was 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...

Comments

[walkingtheline]

This 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 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.

[Porlock Junior]

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.

[Jon Fernquest]

It certainly seems to describe historical reality pretty well.

Cycles of endless endemic warfare, then suddenly miraculous peace, e.g.Iceland (c. 930-1262) or Burma (c. 1270-1600) or the Middle East now:

"...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.

[John Emerson]

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.

[John Emerson]

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.

[Ponzi Q. Globalization]

" 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."

For most Americans, either the negative payoffs don't exist (not many have relatives or friends who are doing the actual fighting) or they aren't understood (wasting $1000 is a bad thing, wasting $700,000,000,000 is a statistic, the worsening of our geo-political situation and the increasing of danger).

The positive payoffs, on the other hand, are always there. For most these are: entertainment value, lessening of fear, vicarious thrill of kicking a bad guy's ass, increase in sense of self-worth from righting some of the world's wrongs, elation on being part of a group that dominates others. And for some, the positives are more: war profiteering and political gain.

Who wouldn't choose the strategy of war?

[Justin Dylan]

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).

[John Emerson]

Jesus, this guy has enemies.

[Anderson]

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.

[David Cameron]

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.

[walkingtheline]

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.

[steve]

More from Binmore here:
http://jasss.soc.surrey.ac.uk/1/1/review1.html

He does credit Axelrod/Rapoport/TFT with introducing the idea that altruism might arise from evolutionary selection. As pointed out already, it isn't a dominant strategy, as is often asserted.

Personally, I discovered Rapoport via his intro to On War, which I found quite lucid.

[David Lloyd-Jones]

I had the good fortune to take Rapoport's course at University of Toronto in the late '80's. We had great fun goofing around in his office after classes (we had working friends in common, and twenty-five years earlier I had been part of the University of Michigan mafia who took him seriously early on), but he sadly gave me a C in the course.

Over a complex solution of mine, printed out on an early personal computer with huge numerical tables, he shook his head and said "David, I can't understand how such an intelligent man can do such bad work. Sometimes things really are as simple as they look."

I think he got good mileage out of applying that apercu to the larger world as well.

[PaulC]

John Emerson: "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."

I agree that counterintuitiveness is not a necessary condition of good work (though I doubt this is the first time somebody has made it into one). Any correct, pertinent result backed by empirical evidence and rigorous analysis is good science.

But I would argue that a true, counterintuitive result on any issue is more valuable than a true result that matches intuition on the same issue. The reason is that people are going to act in accordance with intuition (common sense) whether or not there is any research to back it up. But a policy that is counterintuitive requires some other kind of backing (ideally it should be sound research, though superstition and sheer contrariness can also have this effect in practice--e.g. people might have practiced bloodletting to cure a disease neither because it was backed by evidence nor because it was a particularly intuitive course of action, but other medical practices are counterintuitive and effective; if we stuck to the intuitive we'd lose many opportunities for cures).

It's an unfortunate tendency of academia (and not just economics) to hold up counterintuitiveness as the most important measure of the quality of a result. Some people would rather have a complex and surprising answer to a problem when an ordinary, fairly obvious one would do. But I think that part of the whole business of research is to surprise. It would take most of the fun out of research if every new result merely backed up what everyone believed already.

[John Emerson]

A lawyer who gets a guilty client off is a better lawyer than one who gets an innocent client off, too. But this is a very slippery principle.

[andres]

"A lawyer who gets a guilty client off is a better lawyer than one who gets an innocent client off, too. But this is a very slippery principle."

Not if you include some ethics in the definition of what makes a better lawyer. If he knew with certainty from the beginning that his client was guilty, getting an acquittal does not make him a better lawyer. Similarly, if a prosecutor knows with certainty that the defendant is innocent, then using his abilities to get an erroneous guilty verdict does not make him a better lawyer. Maybe I'm naive, but I don't think of the trial process as being similar to a chess game, and believe that a lawyer's commitment to truth should outweigh his commitment to a "winning" outcome. Game theory needs to reflect this principle on occasion by factoring in utility functions that include altruism and personal integrity.

[John Emerson]

Anders, law is pretty amoral. The best lawyer, within the rules of the law itself, does his best to get a guilty client off.

I was making a comparison to the idea that "The smartest economist is one who proves something counterintuitive"., making the point that that's a sort of skewed way of defining the profession, and that economists are far too biased in that direction.

I personally don't recommend using either econ or law as a model.

[John Emerson]

Anders, law is pretty amoral. The best lawyer, within the rules of the law itself, does his best to get a guilty client off.

I was making a comparison to the idea that "The smartest economist is one who proves something counterintuitive"., making the point that that's a sort of skewed way of defining the profession, and that economists are far too biased in that direction.

I personally don't recommend using either econ or law as a model.

[Barkley Rosser]

Now here is a completely off the wall question/point. Does anybody know his relationship, if any, to fellow game theorist Amon Rapaport?

I have a pet peeve about the trend to journals insisting on References only use authors' initials. I know of at least four pairs of economists who have write (or wrote) in the same area, have the same initials, but have different first initials.

Anatol Rapaport
Amnon Rapaport

John Kenneth Galbraith
James Kenneth Galbraith

Robert E. Baldwin
Richard E. Baldwin

Robert Gordon
Roger Gordon.

The last three of these pairs are father/son combinations.

[radek]

"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)."

This plays a big role in Avner Grief's pretty famous paper on the 11th century Maghribi traders - they used what you call strong recoprocity - but were eventually displaced by, Genoans if I remember correctly, who basically used the simple reciprocity approach. The point of the paper is that different strategies work relatively better or worse in different environmental/cultural/institutional environments.

Here's a link to the abstract
http://links.jstor.org/sici?sici=0022-0507(198912)49%3A4%3C857%3ARACIMT%3E2.0.CO%3B2-M
and Grief's also got a book on the topic.

[Barkley Rosser]

radek,

The usual new institutionalist take on the whole Greif argument is that it ends up being a matter of relevant transactions costs involved as to which predominates. As exchange becomes more widespread and more impersonal, the strong reciprocity conditions tend to weaken, and the transactions costs for the simple reciprocity tend to dominate.

[David Lloyd-Jones]

Barkley,

It's "Rapoport," two p's, two o's.

-dlj.

[Barkley Rosser]

dlj,

Good point. You are right, and I am mistaken.

So, "A. Rappaport" can be easily distinguished from "A. Rapaport," with neither of them being relatives either, presumably, although both are (were) game theorists.

[Barkley Rosser]

dlj,

I take it back. You are wrong. Brad (who spelled it "Rapaport") and I are right. What may have you confused is that there have been quite a few people who have mistakenly spelled it "Rappaport," so that you may have read that somewhere. I suggest googling both spellings. You will quickly see that while "Rappaport" shows up some actual references to him, the single p upfront spelling is indeed the correct one.

So, still, does anybody out there know what, if any, is the relationship between Amnon and Anatol Rapaport, please?