John Nash's notion of equilibrium is ubiquitous in economic theory, but a new study shows that it is often impossible to reach efficiently.
In 1950, John Nash — the mathematician later featured in the book and film "A Beautiful Mind" — wrote a two-page paper that transformed the theory of economics. His crucial, yet utterly simple, idea was that any competitive game has a notion of equilibrium: a collection of strategies, one for each player, such that no player can win more by unilaterally switching to a different strategy.
Nash's equilibrium concept, which earned him a Nobel Prize in economics in 1994, offers a unified framework for understanding strategic behavior not only in economics but also in psychology, evolutionary biology and a host of other fields. Its influence on economic theory "is comparable to that of the discovery of the DNA double helix in the biological sciences," wrote Roger Myerson of the University of Chicago, another economics Nobelist.
When players are at equilibrium, no one has a reason to stray. But how do players get to equilibrium in the first place? In contrast with, say, a ball rolling downhill and coming to rest in a valley, there is no obvious force guiding game players toward a Nash equilibrium.
"Economists have proposed mechanisms for how you can converge [quickly] to equilibrium," said Aviad Rubinstein, who is finishing a doctorate in theoretical computer science at the University of California, Berkeley. But for each such mechanism, he said, "there are simple games you can construct where it doesn't work."
It's always nice to see another win in the game theory column. The iterated prisoner's dilemma triumphs again!
Seriously, this has big ramifications for economics. I think in the same way that W. Brian Arthur re-defined Adam Smith's theory of the 'Ideal Agent'.
Read the article at quantamagazine.org:
(Score: 2) by jmorris on Friday October 06 2017, @02:29PM (1 child)
No, it was an information theory proof that no single leader, central committee or even hyperintelligent AI governing an entity the size of a modern nation state could possibly have enough up to date information to adequately plan if it is operating within the constraints of this universe and dealing with people in meatspace. People are simply too chaotic to make a proper five year plan for. I.e. it would have to be a god with the omniscience power. So anybody proposes Socialism just hit em with the Ghostbuster's question, "Are you a god?"
(Score: 2) by maxwell demon on Friday October 06 2017, @04:14PM
You think the only possible alternatives are central planning socialism as totally unregulated markets? Think again.
The claim I responded to wasn't that markets work better than socialism; the claim was that a completely unregulated free market (something different from the free markets we currently have in Western societies!) works better than anything else (including things that no man has ever thought of).
The Tao of math: The numbers you can count are not the real numbers.