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by Merry Walker on October 19th, 2005

Merry Walker

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In layman's terms, what is the basic premise of John Nash's Nobel prize winning work Equilibrium?

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  • by jalex137 on October 25th, 2005

    jalex137

    The Wikipedia article on the Nash Equilibrium puts it pretty well:
    "In game theory, the Nash equilibrium (named after John Nash who proposed it) is a kind of optimal collective strategy in a game involving two or more players, where no player has anything to gain by changing only their own strategy. If each player has chosen a strategy and no player can benefit by changing their strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium."

    http://en.wikipedia.org/wiki/Nash_equilibrium

    Unfortunately, MW, that may be about as close to layman's terms as it can get. Game theory--and I don't claim to be anything other than a layman myself--is used to describe much more than just games. It applies to the study of economics, politics, international relations, any situation where two or more entities have interests which are opposing or conflicting. The description of each "player's" possible strategy in either terms of getting everything he wants, losing it all, or splitting some less-than-complete benefit with his opponents; and the mathematical analysis of the probablilities of each, can get quite complicated.

    In my understanding, then, the Nash Equilibrium exists when, by this mathematical analyisis, no player, simply by changing his strategy, can gain an advantage which will pressure any other player to change his strategy. It doesn't factor in the possibility of negotiation, appealing to one's goodwill, or other intangibles. The old Cold War theory of Mutual Assured Destruction may have been one of those cases.

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  • by Anonymous on October 2nd, 2009

    Anonymous

    One use of the nash equilibrium is in projecting stock market price levels. This must be proceeded by the determination of the geometric algebraic equation for the existing recent price history.

    While it may be helpful to use curve smoothing, the form is always determined to be a parabola or inversely, an upside down parabola whenever the market is conforming to the nash equibralium. It will only shift to a different shaped parabola when market forces are interrupted, such as the recent financial market scandals. Even then the new parabola will eventually return to the original parabola. This shift is caused by significant market forces whose source is not immediately determinate.

    Observations have shown that these disruptions are short in duration, intuitively due to strong opposing market forces.

    This is helpful in planning mid to long term strategy for managing savings and investments to maximize returns. Once this methodology is understood, it can be used intuitively by observing charts of individual stocks or more accurately, stock indices.

    I doubt that nash was thinking of the future practical and valuable uses of his equilibrium theory; rather his interest was in the mathimatical expressions of the game theory.

    It was to be a long evolution before discovery of many of the uses of this equilibrium due to the complexity of the mathematics involved. I have found that few understand the complex mathematics and are interested in practical applications. Those few that do understand, hold these ideas closely, because it involves valuable intellectual wealth.

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  • by ptosis on June 29th, 2010

    ptosis

    This is the most popular concept of game theory because of the movie "A beautiful mind." To fkg bad the blonde/brunnete example is NOT a nash Equilibrium.

    All it means is the best choice for the individual - because it's a non-cooperative situation...

    Another Nash example is the prisoner's dilemma:


    T = Temptation to defect
    R = Reward for mutual cooperation
    P = Punishment
    S = Sucker's payoff

    More @ http://hubpages.com/h_012/ub/Intro2Games

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