A fixed point theorem for discontinuous functions

P. Jean-Jacques Herings,Gerard Van Der Laan,A J J Talman,Zaifu Yang

Operations Research Letters（2008）

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摘要

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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关键词

gross direction,non-empty polytope,special case,fixed point,discontinuous function,discontinuous games,47h10,fixed point property,discontinuity,continuous function,simplicial subdivision,non-cooperative game theory,65k10,91a10,fixed point theorem

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