Equilibria and strict equilibria of multivalued maps on noninvariant sets
Volume 82 / 2003
Annales Polonici Mathematici 82 (2003), 19-37
MSC: Primary 54C60; Secondary 34A60, 54C65, 47H04.
DOI: 10.4064/ap82-1-3
Abstract
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.
