A Fixed Point Theorem for Discontinuous Functions

P.J.J. Herings; G. van der Laan; A.J.J. Talman; Z. Yang

doi:10.1016/j.orl.2007.03.008

A Fixed Point Theorem for Discontinuous Functions

P.J.J. Herings^*, G. van der Laan, A.J.J. Talman, Z. Yang

^*Corresponding author for this work

Microeconomics & Public Economics

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

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.

Original language	English
Pages (from-to)	89-93
Number of pages	4
Journal	Operations Research Letters
Volume	36
DOIs	https://doi.org/10.1016/j.orl.2007.03.008
Publication status	Published - 1 Jan 2008

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title = "A Fixed Point Theorem for Discontinuous Functions",

abstract = "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.",

author = "P.J.J. Herings and {van der Laan}, G. and A.J.J. Talman and Z. Yang",

year = "2008",

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journal = "Operations Research Letters",

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AU - Herings, P.J.J.

AU - van der Laan, G.

AU - Talman, A.J.J.

AU - Yang, Z.

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Y1 - 2008/1/1

N2 - 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.

AB - 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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DO - 10.1016/j.orl.2007.03.008

M3 - Article

SN - 0167-6377

VL - 36

SP - 89

EP - 93

JO - Operations Research Letters

JF - Operations Research Letters

ER -

A Fixed Point Theorem for Discontinuous Functions

Abstract

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