Stories
Slash Boxes
Comments

SoylentNews is people

posted by Fnord666 on Thursday October 05 2017, @06:24PM   Printer-friendly
from the no-free-rides dept.

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:


Original Submission

 
This discussion has been archived. No new comments can be posted.
Display Options Threshold/Breakthrough Mark All as Read Mark All as Unread
The Fine Print: The following comments are owned by whoever posted them. We are not responsible for them in any way.
  • (Score: 1) by khallow on Thursday October 05 2017, @08:01PM (3 children)

    by khallow (3766) Subscriber Badge on Thursday October 05 2017, @08:01PM (#577606) Journal
    That's the basic Nash equilibrium though it's rather the collective strategy that results in the largest guaranteed minimum payout for each player. The catch is that you are limited in what you can learn about payoffs for the choices given from previous plays (and possibly announcements by the players as well). It claimed in the paper to be already a known result that the minimum number of plays to learn the Nash equilibrium is an exponential function of the number of players n or roughly O(e^n). What they show is that even if you try for an approximate equilibrium rather than go all the way, it's still O(e^n). That's not much of an issue, if you have say, 3 players in your game, but it's totally unmanageable in a million person game.

    They've already indicated what they think the next step will be, namely, classifying games that have good behavior in this regard. In addition, this might lead to ways to perturb the game to a new form that is more stable (perhaps, implement some sort of UBI (universal basic income) rule where a fraction of what is gained/lost is then distributed equally between all players).
  • (Score: -1, Flamebait) by Anonymous Coward on Thursday October 05 2017, @09:23PM

    by Anonymous Coward on Thursday October 05 2017, @09:23PM (#577642)

    So what you saying shitty Socialism for entire population of America is impossible because e^300,000,000. I could have told you that.

  • (Score: 0) by Anonymous Coward on Friday October 06 2017, @07:26AM (1 child)

    by Anonymous Coward on Friday October 06 2017, @07:26AM (#577865)

    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

      by Anonymous Coward on Friday October 06 2017, @07:28AM (#577867)

      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.

      Oh, forgot to mention. That's demonstrably the current strategy our political leaders are playing.