Nash's Math Gets More Beautiful: Even with Infinite Choices, Games May Have Stable Strategies

By Barry, Patrick | Science News, November 8, 2008 | Go to article overview

Nash's Math Gets More Beautiful: Even with Infinite Choices, Games May Have Stable Strategies


Barry, Patrick, Science News


Life's a game, or at least treating it like a game mathematically can be a powerful way to explain the choices people make. John Nash, the mentally troubled mathematician depicted in the book and movie A Beautiful Mind, discovered one of the bedrock theories for understanding competitive interactions (genetically called "games") in which players have a limited set of choices.

Now mathematicians are expanding Nash's idea to cases when the players' options are infinite. Under certain conditions, infinite-choice games are guaranteed to have at least one scenario in which each player's choice gets that player the best deal possible (given everyone else's choices), according to a proof to be published in the February 2009 Nonlinear Analysis.

Such a scenario is called a Nash equilibrium. It is stable because no player can do any better by changing strategy. Like a rock at the bottom of a valley, a game reaching this stable scenario should tend to stay that way. In a sense, it's the fate of the game to end up at a Nash equilibrium, and this predictive power is why Nash's ideas have become widely used in economics and other social sciences.

Nash proved that there is always at least one such equilibrium for games with a finite number of strategic choices. But not all possible games are so limited.

"There are many economically important games in which the sets of pure strategies are infinite," comments Andy McLennan, a mathematician and economist who studies game theory at the University of Queensland campus in St. …

The rest of this article is only available to active members of Questia

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Note: primary sources have slightly different requirements for citation. Please see these guidelines for more information.

Cited article

Nash's Math Gets More Beautiful: Even with Infinite Choices, Games May Have Stable Strategies
Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this article
  • Highlights & Notes
  • Citations
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Search by... Author
    Show... All Results Primary Sources Peer-reviewed

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.