Thursday, August 02, 2012

A game changer?

A new paper by William Press and Freeman Dyson is drawing a lot of attention (via Steven Hsu who also links to relevant papers). From the summary by William Poundstone:
"Executive summary: Robert Axelrod's 1980 tournaments of iterated prisoner's dilemma strategies have been condensed into the slogan, Don't be too clever, don't be unfair. Press and Dyson have shown that cleverness and unfairness triumph after all."
From a response by KARL SIGMUND & MARTIN NOWAK:
"With their splendidly 'mischievous' extortionate strategies, Press and Dyson contribute to classical game theory, by considering two players who grapple with each other in a kind of mental jiu-jitsu. The leverage afforded by zero-determinant strategies offers a splendid new arsenal of throws, locks, and holds.

Which of these strategies can flourish in an evolutionary setting is less clear. Being successful, in this context, feeds back at the population level. It means that more and more players will act like you, be they your offspring or your epigones. Thus you are increasingly likely to encounter your own kind. If your 'extortionate' strategy guarantees that you do twice as well as your opponent, and your opponents' strategy guarantees that she does twice as well as you, this only means that both get nothing. The only norm which is not self-defeating through population dynamics requires players to guarantee each other as much as themselves. We are then back to Tit For Tat. Press and Dyson are perfectly aware of this, of course. In a nutshell, they have uncovered a vast set of strategies linking the scores of two players deterministically (as TFT does), but asymmetrically (unlike TFT). This enriches the canvas of individual interactions, but not necessarily the range of outcomes open to evolving populations."

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