Abstract
An extension of Woodall’s theorem on the satisfactory point to arbitrary continuous functions, as well as a short proof of it, is presented. An extension of Kulpa’s theorem is also made. As application, proofs of the existence of the core payoff in the matching game studied by Alkan and Gale (1990), for arbitrary continuous functions (not only decreasing) and Bapat’s permutation-based generalization of Brouwer’s fixed point theorem, are given.
The research reported in this paper is supported by the KBN Grant No. 2 P03A 017 11.
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© 1999 Springer-Verlag Berlin Heidelberg
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Idzik, A. (1999). The existence of the satisfactory point. In: Alkan, A., Aliprantis, C.D., Yannelis, N.C. (eds) Current Trends in Economics. Studies in Economic Theory, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03750-8_14
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DOI: https://doi.org/10.1007/978-3-662-03750-8_14
Publisher Name: Springer, Berlin, Heidelberg
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