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A fixed point theorem for discontinuous functions

✍ Scribed by P. Jean-Jacques Herings; Gerard van der Laan; Dolf Talman; Zaifu Yang

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
153 KB
Volume
36
Category
Article
ISSN
0167-6377

No coin nor oath required. For personal study only.

✦ Synopsis

Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory.

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