Equivalence results between Nash equilibrium theorem and some fixed point theorems

Abstract We show that the Kakutani and Brouwer fixed point theorems can be obtained by directly using the Nash equilibrium theorem. The corresponding set-valued problems, such as the Kakutani fixed point theorem, Walras equilibrium theorem (set-valued excess demand function), and generalized variati...
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Gespeichert in:

Autor*in:	Yu, Jian [verfasserIn] Wang, Neng-Fa [verfasserIn] Yang, Zhe [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	Brouwer fixed point theorem Kakutani fixed point theorem Nash equilibrium theorem Walras equilibrium theorem KKM lemma variational inequality

Übergeordnetes Werk:	Enthalten in: Fixed point theory and applications - Heidelberg : Springer, 2004, 2016(2016), 1 vom: 24. Juni
Übergeordnetes Werk:	volume:2016 ; year:2016 ; number:1 ; day:24 ; month:06

Links:	Volltext

DOI / URN:	10.1186/s13663-016-0562-z

Katalog-ID:	SPR032137850

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520			\|a Abstract We show that the Kakutani and Brouwer fixed point theorems can be obtained by directly using the Nash equilibrium theorem. The corresponding set-valued problems, such as the Kakutani fixed point theorem, Walras equilibrium theorem (set-valued excess demand function), and generalized variational inequality, can be derived from the Nash equilibrium theorem, with the aid of an inverse of the Berge maximum theorem. For the single-valued situation, we derive the Brouwer fixed point theorem, Walras equilibrium theorem (single-valued excess demand function), KKM lemma, and variational inequality from the Nash equilibrium theorem directly, without any recourse.
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spelling	10.1186/s13663-016-0562-z doi (DE-627)SPR032137850 (SPR)s13663-016-0562-z-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 31.46 bkl 31.65 bkl Yu, Jian verfasserin aut Equivalence results between Nash equilibrium theorem and some fixed point theorems 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We show that the Kakutani and Brouwer fixed point theorems can be obtained by directly using the Nash equilibrium theorem. The corresponding set-valued problems, such as the Kakutani fixed point theorem, Walras equilibrium theorem (set-valued excess demand function), and generalized variational inequality, can be derived from the Nash equilibrium theorem, with the aid of an inverse of the Berge maximum theorem. For the single-valued situation, we derive the Brouwer fixed point theorem, Walras equilibrium theorem (single-valued excess demand function), KKM lemma, and variational inequality from the Nash equilibrium theorem directly, without any recourse. Brouwer fixed point theorem (dpeaa)DE-He213 Kakutani fixed point theorem (dpeaa)DE-He213 Nash equilibrium theorem (dpeaa)DE-He213 Walras equilibrium theorem (dpeaa)DE-He213 KKM lemma (dpeaa)DE-He213 variational inequality (dpeaa)DE-He213 Wang, Neng-Fa verfasserin aut Yang, Zhe verfasserin aut Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2016(2016), 1 vom: 24. Juni (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2016 year:2016 number:1 day:24 month:06 https://dx.doi.org/10.1186/s13663-016-0562-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.46 ASE 31.65 ASE AR 2016 2016 1 24 06
allfields_unstemmed	10.1186/s13663-016-0562-z doi (DE-627)SPR032137850 (SPR)s13663-016-0562-z-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 31.46 bkl 31.65 bkl Yu, Jian verfasserin aut Equivalence results between Nash equilibrium theorem and some fixed point theorems 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We show that the Kakutani and Brouwer fixed point theorems can be obtained by directly using the Nash equilibrium theorem. The corresponding set-valued problems, such as the Kakutani fixed point theorem, Walras equilibrium theorem (set-valued excess demand function), and generalized variational inequality, can be derived from the Nash equilibrium theorem, with the aid of an inverse of the Berge maximum theorem. For the single-valued situation, we derive the Brouwer fixed point theorem, Walras equilibrium theorem (single-valued excess demand function), KKM lemma, and variational inequality from the Nash equilibrium theorem directly, without any recourse. Brouwer fixed point theorem (dpeaa)DE-He213 Kakutani fixed point theorem (dpeaa)DE-He213 Nash equilibrium theorem (dpeaa)DE-He213 Walras equilibrium theorem (dpeaa)DE-He213 KKM lemma (dpeaa)DE-He213 variational inequality (dpeaa)DE-He213 Wang, Neng-Fa verfasserin aut Yang, Zhe verfasserin aut Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2016(2016), 1 vom: 24. Juni (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2016 year:2016 number:1 day:24 month:06 https://dx.doi.org/10.1186/s13663-016-0562-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.46 ASE 31.65 ASE AR 2016 2016 1 24 06
allfieldsGer	10.1186/s13663-016-0562-z doi (DE-627)SPR032137850 (SPR)s13663-016-0562-z-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 31.46 bkl 31.65 bkl Yu, Jian verfasserin aut Equivalence results between Nash equilibrium theorem and some fixed point theorems 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We show that the Kakutani and Brouwer fixed point theorems can be obtained by directly using the Nash equilibrium theorem. The corresponding set-valued problems, such as the Kakutani fixed point theorem, Walras equilibrium theorem (set-valued excess demand function), and generalized variational inequality, can be derived from the Nash equilibrium theorem, with the aid of an inverse of the Berge maximum theorem. For the single-valued situation, we derive the Brouwer fixed point theorem, Walras equilibrium theorem (single-valued excess demand function), KKM lemma, and variational inequality from the Nash equilibrium theorem directly, without any recourse. Brouwer fixed point theorem (dpeaa)DE-He213 Kakutani fixed point theorem (dpeaa)DE-He213 Nash equilibrium theorem (dpeaa)DE-He213 Walras equilibrium theorem (dpeaa)DE-He213 KKM lemma (dpeaa)DE-He213 variational inequality (dpeaa)DE-He213 Wang, Neng-Fa verfasserin aut Yang, Zhe verfasserin aut Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2016(2016), 1 vom: 24. Juni (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2016 year:2016 number:1 day:24 month:06 https://dx.doi.org/10.1186/s13663-016-0562-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.46 ASE 31.65 ASE AR 2016 2016 1 24 06
allfieldsSound	10.1186/s13663-016-0562-z doi (DE-627)SPR032137850 (SPR)s13663-016-0562-z-e DE-627 ger DE-627 rakwb eng 510 ASE 510 ASE 31.46 bkl 31.65 bkl Yu, Jian verfasserin aut Equivalence results between Nash equilibrium theorem and some fixed point theorems 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We show that the Kakutani and Brouwer fixed point theorems can be obtained by directly using the Nash equilibrium theorem. The corresponding set-valued problems, such as the Kakutani fixed point theorem, Walras equilibrium theorem (set-valued excess demand function), and generalized variational inequality, can be derived from the Nash equilibrium theorem, with the aid of an inverse of the Berge maximum theorem. For the single-valued situation, we derive the Brouwer fixed point theorem, Walras equilibrium theorem (single-valued excess demand function), KKM lemma, and variational inequality from the Nash equilibrium theorem directly, without any recourse. Brouwer fixed point theorem (dpeaa)DE-He213 Kakutani fixed point theorem (dpeaa)DE-He213 Nash equilibrium theorem (dpeaa)DE-He213 Walras equilibrium theorem (dpeaa)DE-He213 KKM lemma (dpeaa)DE-He213 variational inequality (dpeaa)DE-He213 Wang, Neng-Fa verfasserin aut Yang, Zhe verfasserin aut Enthalten in Fixed point theory and applications Heidelberg : Springer, 2004 2016(2016), 1 vom: 24. Juni (DE-627)379482037 (DE-600)2135860-6 1687-1812 nnns volume:2016 year:2016 number:1 day:24 month:06 https://dx.doi.org/10.1186/s13663-016-0562-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 31.46 ASE 31.65 ASE AR 2016 2016 1 24 06
language	English
source	Enthalten in Fixed point theory and applications 2016(2016), 1 vom: 24. Juni volume:2016 year:2016 number:1 day:24 month:06
sourceStr	Enthalten in Fixed point theory and applications 2016(2016), 1 vom: 24. Juni volume:2016 year:2016 number:1 day:24 month:06
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Brouwer fixed point theorem Kakutani fixed point theorem Nash equilibrium theorem Walras equilibrium theorem KKM lemma variational inequality
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container_title	Fixed point theory and applications
authorswithroles_txt_mv	Yu, Jian @@aut@@ Wang, Neng-Fa @@aut@@ Yang, Zhe @@aut@@
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author	Yu, Jian
spellingShingle	Yu, Jian ddc 510 bkl 31.46 bkl 31.65 misc Brouwer fixed point theorem misc Kakutani fixed point theorem misc Nash equilibrium theorem misc Walras equilibrium theorem misc KKM lemma misc variational inequality Equivalence results between Nash equilibrium theorem and some fixed point theorems
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topic_title	510 ASE 31.46 bkl 31.65 bkl Equivalence results between Nash equilibrium theorem and some fixed point theorems Brouwer fixed point theorem (dpeaa)DE-He213 Kakutani fixed point theorem (dpeaa)DE-He213 Nash equilibrium theorem (dpeaa)DE-He213 Walras equilibrium theorem (dpeaa)DE-He213 KKM lemma (dpeaa)DE-He213 variational inequality (dpeaa)DE-He213
topic	ddc 510 bkl 31.46 bkl 31.65 misc Brouwer fixed point theorem misc Kakutani fixed point theorem misc Nash equilibrium theorem misc Walras equilibrium theorem misc KKM lemma misc variational inequality
topic_unstemmed	ddc 510 bkl 31.46 bkl 31.65 misc Brouwer fixed point theorem misc Kakutani fixed point theorem misc Nash equilibrium theorem misc Walras equilibrium theorem misc KKM lemma misc variational inequality
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title	Equivalence results between Nash equilibrium theorem and some fixed point theorems
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title_full	Equivalence results between Nash equilibrium theorem and some fixed point theorems
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title_sort	equivalence results between nash equilibrium theorem and some fixed point theorems
title_auth	Equivalence results between Nash equilibrium theorem and some fixed point theorems
abstract	Abstract We show that the Kakutani and Brouwer fixed point theorems can be obtained by directly using the Nash equilibrium theorem. The corresponding set-valued problems, such as the Kakutani fixed point theorem, Walras equilibrium theorem (set-valued excess demand function), and generalized variational inequality, can be derived from the Nash equilibrium theorem, with the aid of an inverse of the Berge maximum theorem. For the single-valued situation, we derive the Brouwer fixed point theorem, Walras equilibrium theorem (single-valued excess demand function), KKM lemma, and variational inequality from the Nash equilibrium theorem directly, without any recourse.
abstractGer	Abstract We show that the Kakutani and Brouwer fixed point theorems can be obtained by directly using the Nash equilibrium theorem. The corresponding set-valued problems, such as the Kakutani fixed point theorem, Walras equilibrium theorem (set-valued excess demand function), and generalized variational inequality, can be derived from the Nash equilibrium theorem, with the aid of an inverse of the Berge maximum theorem. For the single-valued situation, we derive the Brouwer fixed point theorem, Walras equilibrium theorem (single-valued excess demand function), KKM lemma, and variational inequality from the Nash equilibrium theorem directly, without any recourse.
abstract_unstemmed	Abstract We show that the Kakutani and Brouwer fixed point theorems can be obtained by directly using the Nash equilibrium theorem. The corresponding set-valued problems, such as the Kakutani fixed point theorem, Walras equilibrium theorem (set-valued excess demand function), and generalized variational inequality, can be derived from the Nash equilibrium theorem, with the aid of an inverse of the Berge maximum theorem. For the single-valued situation, we derive the Brouwer fixed point theorem, Walras equilibrium theorem (single-valued excess demand function), KKM lemma, and variational inequality from the Nash equilibrium theorem directly, without any recourse.
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title_short	Equivalence results between Nash equilibrium theorem and some fixed point theorems
url	https://dx.doi.org/10.1186/s13663-016-0562-z
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Equivalence results between Nash equilibrium theorem and some fixed point theorems

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