A fixed point theorem for measurable selection valued correspondences induced by upper Caratheodory correspondences

Fu, Jing and Page, Frank (2023) A fixed point theorem for measurable selection valued correspondences induced by upper Caratheodory correspondences. Journal of Fixed Point Theory and Applications, 25 (1). ISSN 1661-7738

Text (A Fixed Point Theorem for Measurable Selection Valued Correspondences Induced by Upper Caratheodory Correspondences) - Accepted Version Download (253kB)

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Abstract

We show that any measurable selection valued correspondence induced by the composition of an m-tuple of real-valued Caratheodory functions with an upper Caratheodory (uC) correspondence has fixed points if the underlying uC correspondence in the composition contains a continuum valued uC sub-correspondence. As an application, we show that all uncountable-compact discounted stochastic games (DSGs) satisfying the usual assumptions have Nash payoff selection correspondences having fixed points provided of course that the uC Nash correspondence contains a continuum valued uC Nash sub-correspondence. Fu and Page [8] have shown that all such DSGs, in fact, have uC Nash correspondences containing continuum valued uC Nash sub-correspondences—implying, therefore, that all DSGs satisfying the usual assumptions have stationary Markov perfect equilibria.

Item Type:	Article
Official URL:	https://www.springer.com/journal/11784
Additional Information:	© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
Divisions:	Systemic Risk Centre
Subjects:	Q Science > QA Mathematics
Date Deposited:	04 Jan 2023 16:12
Last Modified:	15 Apr 2024 21:33
URI:	http://eprints.lse.ac.uk/id/eprint/117703

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