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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: 2, Disagree) by jmorris on Thursday October 05 2017, @07:57PM (16 children)
This is only shocking for those who attack the strawman version of free market economics. No, a free market will not discover THE optimal distribution of goods, wealth, etc. so long as events keep changing the supply and demand. When extreme events alter the supply or demand faster than the existing market mechanisms can adapt fairly large distortions can appear. It simply does it better than any possible planned economy, and that is a mathematical certainty. And the more free and open the faster and better it converges to a 'good enough' solution. There will always be noise in the signals from the market, but so long as people are free to seek it out and profit from it they will tend to be blips instead of massive distortions.
Yes that means it is better if we don't make laws against profiteering, gouging, scalping, etc.
But it also means we don't let industry collude with government to raise prices, exclude competitors, etc.
It does mean more transparency in the market is always a good thing.
(Score: 2, Informative) by khallow on Thursday October 05 2017, @08:12PM
(Score: 5, Insightful) by Anonymous Coward on Thursday October 05 2017, @08:22PM (6 children)
Strawman version of free market economics? You do realize that the free market theory is itself a massive strawman yes? There is no such thing as a truly free market, the same way that econ 101 suppy/demand curves are quite rarely seen in reality.
Know how to tell when someone is a blowhard?
(Score: 0) by Anonymous Coward on Thursday October 05 2017, @09:25PM (1 child)
That is true, free market can only exist if the consumer has perfect information about the products. It is to the incentive of the producer/seller, and quite frankly the job of Marketing Department to ensure that the customer has no fucking idea what the product actually is.
(Score: 1, Informative) by Anonymous Coward on Thursday October 05 2017, @09:51PM
Not to mention they have motive to not inform the customer of better alternatives, thus causing harm. I wish we were able to move to the post-economic society where profits weren't so central to businesses and the lives of the workers. So much evil is caused by simple spreadsheets.
(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]
(Score: 2) by Wootery on Friday October 06 2017, @08:57AM (2 children)
Unless we value something other than economic optimisation, of course. Which we do. That's the whole point of scalping laws.
(Score: 2) by jmorris on Friday October 06 2017, @03:19PM (1 child)
What do you value? For example if we allowed "gouging" before and after a hurricane, and everyone KNEW it would be the normal situation, prices would go up but so would availability of goods. Do you think this is better or worse?
Example: Hotels are forbidden from raising their prices. What happens? They instantly sell out so people must flee farther and farther looking for a room. Allow the hotels to raise prices and what changes? Instead of booking three rooms for the family everybody crowds into one or two. With a lot of extra money available the hotel can add temp staff to move heaven and earth to bring 100% of their units online (they rarely have them all ready to rent unless it is their known peak season). Result: more people get rooms with less fleeing.
Example: After a hurricane everybody wants a generator. None to be had, they all sold out before the storm hit and the big box stores are in the dark too. People try to bring them in to make a quick buck and get arrested for their efforts. This makes generators a black market good and raises their prices even more until distribution networks get back to a point where big chains can roll truckloads in again. Good for Home Depot that many customers must suffer until they get there, not good for people who would have been willing to pay 50% demand premium for NOW. It would be better to let the market work. A few people will take off work, load a truck with generators and go give them away. Yea, good for them. A lot more would take off work, load up a truck with generators and resell them at a 50% instant markup if they weren't worried about getting a felony arrest record for their trouble. Result: more people get generators. And if it were legal the premium wouldn't stay 50% long, enough people would be using their monster truck / boat, etc. to get generators in that the premium would sink quite a bit.
Non hurricane example: Sports and concert tickets. Nobody likes scalpers. But they are the market solving a problem. For PR reasons tickets are sold at below their market value. Essentially a lottery system preferring people who can stand in line. But people with more productive uses of their time ALSO want tickets are are willing to convert the money earned from that productivity into tickets. Since it isn't legal, the scalpers fill the gap in the marketplace. Admit live events are a finite good, auction the tickets. Knowing and capturing the true market demand would allow additional play dates to be funded, bigger stadiums built, etc.
(Score: 2) by Wootery on Friday October 06 2017, @11:04PM
So you're saying the PR reasons should be ignored and the price should be maximised 'naively'. So you know better than the market, then?
(Score: 2) by maxwell demon on Friday October 06 2017, @09:57AM (2 children)
There is no mathematical certainty about anything involving sentient agents. You may get mathematical certainty with hypothetical ideal agents and hope that the real agents act as they should according to your theory (and you'll inevitably find they don't). Or you may do actual research into the behaviour of people, and improve your model based on the results, which is proper science, but frowned upon by libertarians (maybe because deep inside they know this might debunk their market religion).
The Tao of math: The numbers you can count are not the real numbers.
(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.
(Score: 0) by Anonymous Coward on Friday October 06 2017, @10:59AM (1 child)
And that "transparency in the market", how would it work?
Should the government make laws for it? Would that be interfering in the market?
Will the market reach any equilibrium in the amount of transparency by being "more free and open"?
You seem like a reasonable guy. I'm sure you can infer my general opinion about economics and economists buy thinking about these questions ....
(Score: 2) by jmorris on Friday October 06 2017, @02:37PM
Yes. I'm not an anarchist. There are things government is the best solution to at our current social tech level. Maintaining Rule of Law and maintaining a monopoly on the legitimate use of force are the primary domestic duties. That encompasses promoting standards to simplify trade, from basic weights and measures to financial disclosure for publicly traded entities, collection and open reporting of vital economic statistics, etc. It means detecting and punishing fraud. It can also mean exerting the collective rights of ownership in disputes such as pollution, depending on the situation. "The People" as a class in a class action, the government is our appointed representative, not some ambulance chasing lawyer looking to get rich and leave the "class" holding coupons.