Sunday, February 04, 2007

Anatol Rapoport, 1911-2007

Economist's View notes the passing of Anatol Rapoport, a mathematician turned game theorist and political theorist. I first discovered Rapoport from his introduction to an edition of von Clausewitz's On War. I found the introduction far more lucid and useful than von Clauswitz's own presentation. You can often detect a first rate thinker from a relatively short piece of work, and this brief introduction piqued my interest in Rapoport many years ago. As noted here,

I read some of his 1984 book "Mathematical Methods in the Social and Behavioral Sciences" and it's a great book. There are not many people who have a strong and original mathematical mind and yet know how to apply it with wisdom, but Rapoport's reach and depth in the book is hugely impressive.

Rapoport was the author of Tit for Tat, the benevolent strategy for prisoner's dilemma that won the earliest tournaments conducted by Axelrod at Michigan.

Globe&Mail: That year also saw publication of political scientist Robert Axelrod's seminal book, The Evolution of Co-operation, which asked a simple, yet age-old, question: If living things evolve through competition, how can co-operation ever emerge? A computer tournament was organized to study the relationship of game theory to evolution -- a variation on the Prisoner's Dilemma. Entries came from the world's top theorists.

Dr. Rapoport entered a program he wrote called Tit-For-Tat, consisting of four lines of code. It was by far the simplest entry, and it won. Betraying the retributive implications of its name, the program opened by co-operating with its opponent. Thereafter, it played exactly as the other side had played in the preceding game. If the other side had defected, Tit-For-Tat also defected for that one game. If the other side had co-operated, it co-operated on the next round.

"In effect, Tit-For-Tat punished the other player for selfish behaviour and rewarded her for co-operative behaviour -- but the punishment lasted only as long as the selfish behaviour lasted," observed Metta Spencer, editor of Peace Magazine, on the occasion of Dr. Rapoport's 90th birthday. "This proved to be an exceptionally effective sanction, quickly showing the other side the advantages of co-operating. . . . It also set moral philosophers to proposing this as a workable principle to use in real life interactions."


Seth said...

"Tit-For-Tat ... also set moral philosophers to proposing this as a workable principle"

I had to laugh reading this. Tit for tat is nothing but the Old Testament "an eye for an eye" plus the one-bit choice of initial strategy: start by being generous, which flows obviously from the Gospels.

The idea that a terse algorithmic expression of centuries old wisdom would strike "moral philosophers" as an innovation is hilarious. Technology has that effect on a lot of otherwise intelligent people.

Seth said...

Thanks for calling attention to Rapaport. I plan to look up some of his work.

Steve Hsu said...

But what I think really was a surprise to evolutionary thinkers is how a game as simple as PD could demonstrate the *evolution* of altruism. It also illustrates that the survivability of altruistic strategies depends on the population mix -- too many nasty types and the nice ones die off, but a population with lots of nice TFT players does better overall, and is hard on nasty types. So evolutionary advantage depends a lot on what kind of "society" you are in.

You might think these conclusions are obvious, but they elude a lot of people. The PD game is simple and illustrates all these concepts nicely.

In the original PD tourneys Rapoport really blew everyone else away, and his program was very simple. It shows how nutty the game theorists at the time were about what might work in the real world.

Note that mean strategies can be quite successful as well. See:

Seth said...

I quite agree that Axelrod ran an interesting experiment and that there was some surprise value in finding that very simple, very old ideas could be justified on evolutionary lines, etc.

What I found humorous is simply the process of "life imitating art imitating life". Rapaport applies very elementary moral ideas to an artificial environment, they seem to work as they should and the folks who should have the most confidence and authority in explaining those moral ideas seem to be among the most surprised at their efficacy. Sort of a physician heal thyself moment.

I guess most people are used to thinking of morality as something that has to be taken on faith in the teeth of contrary experience. But surely moral philosophers would also be familiar with 18th century attempts at grounding the same ideas more naturalistically (starting with Kant).

"It shows how nutty the game theorists at the time were about what might work in the real world."

I think any moral philosophers who found this surprising probably were investing energy in a lot of nutty ideas as well.

Anonymous said...

Two centuries ago, t4t was generalized as Reciprocity.

Anonymous said...

Sometimes expressing an old idea in a new way is just what's needed.

Rapoport's main interest in Prisoner's Dilemma was that, in his view, it compels a shift from individual to collective rationality.

Steve Hsu said...

Anthony, are you any relation to Anatol?

Please tell us more, if you are!

Anonymous said...

Yes, I'm his son. I'm working on a collection of some of his unpublished manuscripts (mostly talks he gave) that I'll be making a website for, with comments and discussion boards, etc. Can't say when I'll have it up, but I've got some great material on a lot of subjects. All on paper (even carbon copies!): it'll take some time to digitize.

Steve Hsu said...

Anthony: great! Let us know when the site is up -- I will post a link on my blog :-)

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