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An infinite beautiful mind

Theorem identifies games with infinite choices having at least one Nash equilibrium

By
12:00pm, October 10, 2008

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 (generically called “games”) in which the players have a limited set of choices.

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

Such a scenario — or set of choices for each player — is called a Nash equilibrium and is stable because no player can do any

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