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A Note on fixed point theorems for semi-continuous correspondences on ![$[0,1]$](/proc/1998-126-10/S0002-9939-98-04614-0/gif-title/img1.gif)
Author(s):
Zhou
Wu
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3061-3064.
MSC (1991):
Primary 47H10, 54H25, 90D40;
Secondary 26A15
MathSciNet review:
1469442
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Abstract:
This paper presents a fixed point theorem for correspondences on [0,1]. Some examples comparing it to related work and also some simple applications to game theory are included.
References:
- 1.
- J. Guillerme, Intermediate value theorems and fixed point theorems for semi-continuous functions in product spaces, Proc. Amer. Math. Soc. 123, 2119-2122(1995). MR 95i:54053
- 2.
- E. Klein and A. C. Thompson, Theory of Correspondence: including applications to mathematical economics, John Wiley & Sons, 1984. MR 86a:90012
- 3.
- E. Michael, Continuous selections. I. Ann. of Math. 63 361-382(1956). MR 17:990e
- 4.
- P. Milgrom and J. Roberts, Comparing equilibria, Amer. Econ. Rev. 84, 441-459(1994).
- 5.
- W. L. Strother, On an open question concerning fixed points, Proc. Amer. Math. Soc.4, 988-993 (1953). MR 15:642c
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Additional Information:
Zhou
Wu
Affiliation:
Department of Mathematics, Statistics & Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
Address at time of publication:
Faculty of Computer Science, Daltech, Dalhousie University, P.O. Box 1000, Halifax, Nova Scotia, Canada B3J 2X4
Email:
zwu@cs.dal.ca
DOI:
10.1090/S0002-9939-98-04614-0
PII:
S 0002-9939(98)04614-0
Keywords:
Fixed point,
game theory
Received by editor(s):
September 3, 1996
Received by editor(s) in revised form:
March 17, 1997
Additional Notes:
The author would like to thank Professor S. Dasgupta for inspiring this problem, and Professor K. K. Tan for several discussions.
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1998,
American Mathematical Society
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