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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) by Anonymous Coward on Friday October 06 2017, @07:26AM (1 child)
The biggest problem with Nash's Equilibrium is that Time Exists.
Right NOW the best immediate strategy that floats all boats might not actually be best. I could be playing to lose in the short term, and for the duration of the entire game. Because AFTER I've thrown the game I get a payout from the Mafia in excess of the winnings I could get in the game. The risk of me getting caught even later might factor into it though, and over time I'd have to adopt another strategy, maybe I cut a deal with the other players to completely fuck the game up into some absurd end condition, but that will have us all on top in the long run after we split the pay-offs.
Even if you know the rules of the game and the entire game state, there may be another game happening outside that game who's win state is determined later. Also, you could just be playing for the fuck of it, not caring if you win or lose or get offed by the mobsters because you just got diagnosed with a terminal illness and you'd rather go out with a bang. Maybe, since the PAST exists you're playing to fuck everything up fore everyone, even yourself, just for revenge.
Any game system that can be described must exist in a universe that's larger than the game. Case & Point: People who believe in an afterlife may do some crazy shit in this universe because they believe they're playing a bigger game.
(Score: 0) by Anonymous Coward on Friday October 06 2017, @07:28AM
Oh, forgot to mention. That's demonstrably the current strategy our political leaders are playing.