This paper is concerned with existence of equilibrium of a set-valued map in a given compact subset of a finite-dimensional space. Previously known conditions ensuring existence of equilibrium imply that the set is either invariant or viable for the differential inclusion generated by the set-valued map. We obtain some equilibrium existence results with conditions which imply neither invariance nor viability of the given set. The problem of existence of strict equilibria is also discussed.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-1-3,
author = {Pierre Cardaliaguet and Grzegorz Gabor and Marc Quincampoix},
title = {Equilibria and strict equilibria of multivalued maps on noninvariant sets},
journal = {Annales Polonici Mathematici},
volume = {81},
year = {2003},
pages = {19-37},
zbl = {1099.54018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-1-3}
}
Pierre Cardaliaguet; Grzegorz Gabor; Marc Quincampoix. Equilibria and strict equilibria of multivalued maps on noninvariant sets. Annales Polonici Mathematici, Tome 81 (2003) pp. 19-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap82-1-3/