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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) 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?