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

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  • Fu, Jing
  • Page, Frank

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. Moreover, this composition of the m-tuple of real-valued Caratheodory functions with the continuum valued uC sub-correspondence induces a measurable selection valued sub-correspondence that is weak star upper semicontinuous.

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  • Fu, Jing & Page, Frank, 2022. "A fixed point theorem for measurable selection valued correspondences induced by upper Caratheodory correspondences," LSE Research Online Documents on Economics 119623, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:119623
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    References listed on IDEAS

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    1. Fu, Jing & Page, Frank, 2022. "Parameterized state-contingent games, 3M minimal Nash correspondences, and connectedness," LSE Research Online Documents on Economics 118877, London School of Economics and Political Science, LSE Library.
    2. C. J. Himmelberg & T. Parthasarathy & F. S. VanVleck, 1976. "Optimal Plans for Dynamic Programming Problems," Mathematics of Operations Research, INFORMS, vol. 1(4), pages 390-394, November.
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