In this paper, we introduce some equivalence results of the existence theorem on Brouwer fixed point theorem, Kakutani fixed point theorem, equilibrium points of mathematical economics and Nash equilibrium theorem of game theory.
[1] Border K C. Fixed Point Theorems with Applications to Economics and Game Theory[M]. Cambridge:Cambridge University Press, 1985.
[2] Efe A O K. Real Analysis with Economic Applications[M]. Princeton:Princeton University Press, 2007.
[3] 俞建. 博弈论与非线性分析[M]. 北京:科学出版社, 2008.
[4] Brouwer L. Uber Abbidungen von Mannigfaltigkeiten[J]. Mathematische Annalen, 1912, 71:97-115.
[5] Kakutani S. A generalization of Brouwer's fixed point theorem[J]. Duke Mathematical Journal, 1941, 8:457-459.
[6] 张恭庆,林源渠. 泛函分析讲义(上册)[M]. 北京:北京大学出版社,1987.
[7] Berge C. Topological Spaces[M]. New York:MacMillan, 1963.
[8] 俞建. 博弈论选讲[M]. 北京:科学出版社,2014.
[9] Uzawa H. Walras' existence theorem and Brouwer's fixed point theorem[J]. Economic Studies Quarterly, 1962, 8:59-62.
[10] Gale D. The law of supply and demand[J]. Mathematica Scandinavica, 1955, 3:155-169.
[11] Nikaido H. On the classical multilateral exchange problems[J]. Microeconomica, 1956, 8:135-145.
[12] Debreu G. Market equilibrium[J]. Proceedings of the National Academy of Sciences of the United States of America, 1956, 42(11):876-878.
[13] Komiya H. Inverse of the Berge maximum theorem[J]. Economic Theory, 1997, 9:371-375.
[14] Zhou L. The structure of the Nash equilibrium sets and 2-player games[J]. Rationality and Equilibrium, 2006, 57:57-66.
[15] Yu J, Wang N F, Yang Z. Equivalence results between Nash equilibrium theorem and some fixed point theorems[J]. Fixed Point Theory and Applications, 2016, 69.
[16] 俞建. 有限理性与博弈论中平衡点集的稳定性[M]. 北京:科学出版社,2017.
