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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: 0, Flamebait) by jmorris on Thursday October 05 2017, @09:34PM (3 children)
I have posted a link to a full math proof using information theory, but the general degradation in search (tried google, bing and duck) means it is now out of easy reach for reposting. But it has long been understood that it is a fatal problem in centrally planned economies even before the final math proof was published. Start with Economic Calculation Problem [infogalactic.com] and dig until you are satisfied.
Or you can be a Science denier. Most Progs are now so you have plenty of company. Here in Clown World as we hurtle toward a split it looks like the Progs are taking the NFL and the Right is taking Science in the great national divorce settlement. Who would have seen that coming?
(Score: 2, Insightful) by Anonymous Coward on Thursday October 05 2017, @09:47PM
Only if you believe the media narratives, which I guess is why so many people are upset about the NFL protests. Grow up.
There is no mathematically perfect models of economics, QED you're still a blowhard. I'm not advocating a centrally planned economy, or saying we must be rid of capitalism FOREVER. My personal feeling is that almost all the models should be used where they make the most sense. Workers should own the businesses they work at, but otherwise nothing should really change for most private businesses. Some ventures should be tax funded since a profit motive is anathema to their ideals (medical care, prison, basic infrastructure, parks). Some amount of central planning is a good thing, the US is for the most part a massive study on poorly planned urban development. Government regulation is at times very very necessary to prevent profit motives from causing excessive harm to the environment, public health, the economy at large.
One day crazy divisive people such as yourself will either finally "get it" or you'll fade into obscurity as the old guy yelling at commie kids and how things were so much better "back in the day". Then you'll roll into the local hospital to get your hip surgery for free and cluelessly continue your ranting.
(Score: 2) by linuxrocks123 on Thursday October 05 2017, @10:56PM
That's really a shame you couldn't find the proof. Even though you're probably (okay, almost definitely) misrepresenting what it is, it still would have been interesting.
(Score: 1, Interesting) by Anonymous Coward on Thursday October 05 2017, @11:16PM
I think you may be referring to the below link, however some commentators mention that the problem goes away when you use sparsely linked matrixes which are more accurate representations of production capacity and requirements (Apparently. I am sufficiently ignorant of the topic to have no opinion one way or the other)
http://crookedtimber.org/2012/05/30/in-soviet-union-optimization-problem-solves-you/ [crookedtimber.org]
Also given your history of some rather Austrian school comments, you may want to have a look at the below which rather puts a puncture in the idea of price signalling
http://evonomics.com/hayek-meets-information-theory-fails/ [evonomics.com]