Fixed Points and Equilibria

  • Eric V. DenardoEmail author
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 149)


In 1909, L. E. J. Brouwer proved a fixed point theorem that is illustrated by this scenario: At dawn, the surface of an oval swimming pool is perfectly still. Then a breeze begins to blow. The wind is strong enough to create waves, but not breakers. At dusk, the wind dies down, and the surface becomes still again. Each point on the surface of the pool may have shifted continuously during the day, but each point that began on the surface remains there throughout the day. Brouwer’s theorem guarantees that at least one point on the surface ends up where it began.


Distinguished Point Convex Combination Affine Space Unit Simplex Column Player 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Yale UniversityNew HavenUSA

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