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Infimum Principle
Author(s):
Wladyslaw
Kulpa;
Andrzej
Szymanski
Journal:
Proc. Amer. Math. Soc.
132
(2004),
203-210.
MSC (1991):
Primary 52A07, 54H25, 90A56;
Secondary 90D06
Posted:
May 28, 2003
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Abstract:
We utilize the technique of dual sets to prove a theorem on the attainment of a simultaneous infimum by a compatible family of functions. Corollaries to the theorem include, among others, the von Neumann Minimax Principle and Nash's Equilibrium Theorem.
References:
- 1.
- K. Devlin, Mathematician Awarded Nobel Prize, FOCUS 14 (6) (1994), 1, 3.
- 2.
- D. Gale, John Nash and the Nobel Prize, FOCUS 15 (2) (1995), 4.
- 3.
- D. Gale, The law of supply and demand, Math. Scandinavia 3 (1955), 155-169. MR 17:985f
- 4.
- J. Dugundji and A. Granas, Fixed Point Theory, vol. 1, Polish Scientific Publishers, Warszawa 1982. MR 83j:54038
- 5.
- W. Kulpa, Convexity and the Brouwer Fixed Point Theorem, Topology Proceedings, 22(1997), 211-235. MR 2000h:54068
- 6.
- J. F. Nash, Equilibrium points in
 -person games, Proc. Nat. Acad. Sci. USA 36 (1950), 48-49. MR 11:192c - 7.
- J. F. Nash, Non-cooperative games, Annals of Math. 54 (1951), 286-295. MR 13:261g
- 8.
- H. Nikaido, Convex Structures and Economic Theories, Mathematics in Science and Engineering, vol. 51, Academic Press, 1968. MR 43:2970
- 9.
- H. Nikaido, On the classical multilateral exchange problem, Metroeconomics 8 (1956), Fas. 2. MR 18:266a
- 10.
- H. Reitberger, Vietoris-Beglesches Abbildungstheorem, Vietoris-Lefschetz-Eilenberg-Mont- gomery-Beglescher Fixpunktsatz und Wirtschaftsnobelpreise, Jahresbericht der Deutschen Mathematicer-Vereinigung 103.3(2001), 67-73. MR 2002m:91016
- 11.
- J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, John Wiley & Sons, New York, 1964.
- 12.
- N. N. Vorob'ev, Game Theory: Lectures for Economists and Systems Scientists, Applications of Mathematics, vol. 7, Springer-Verlag, 1977. MR 56:10752
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Additional Information:
Wladyslaw
Kulpa
Affiliation:
Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland
Email:
kulpa@ux2.math.us.edu.pl
Andrzej
Szymanski
Affiliation:
Department of Mathematics, Slippery Rock University, Slippery Rock, Pennsylvania 16057
Email:
andrzej.szymanski@sru.edu
DOI:
10.1090/S0002-9939-03-06994-6
PII:
S 0002-9939(03)06994-6
Keywords:
Simplicial space,
dual family,
fixed point
Received by editor(s):
November 14, 2001
Received by editor(s) in revised form:
August 14, 2002
Posted:
May 28, 2003
Communicated by:
Alan Dow
Copyright of article:
Copyright
2003,
American Mathematical Society
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