Geodesic
Equilibria and strict equilibria of multivalued maps on noninvariant sets
Pierre Cardaliaguet1 ; Grzegorz Gabor2 ; Marc Quincampoix1
1 Laboratoire de Mathématiques Université de Bretagne Occidentale 6, avenue Victor Le Gorgeu B.P. 809 29285 Brest Cedex, France
2 Laboratoire de Mathématiques Université de Bretagne Occidentale 6, avenue Victor Le Gorgeu B.P. 809 29285 Brest Cedex, France and Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland
Annales Polonici Mathematici, Tome 82 (2003) no. 1, pp. 19-37.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ap82-1-3
Keywords: paper concerned existence equilibrium set valued map given compact subset finite dimensional space previously known conditions ensuring existence equilibrium imply set either invariant viable differential inclusion generated set valued map obtain equilibrium existence results conditions which imply neither invariance nor viability given set problem existence strict equilibria discussed

Pierre Cardaliaguet 1 ; Grzegorz Gabor 2 ; Marc Quincampoix 1

1 Laboratoire de Mathématiques Université de Bretagne Occidentale 6, avenue Victor Le Gorgeu B.P. 809 29285 Brest Cedex, France
2 Laboratoire de Mathématiques Université de Bretagne Occidentale 6, avenue Victor Le Gorgeu B.P. 809 29285 Brest Cedex, France and Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland 
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Pierre Cardaliaguet; Grzegorz Gabor; Marc Quincampoix. Equilibria and strict equilibria of multivalued
 maps on noninvariant sets. Annales Polonici Mathematici, Tome 82 (2003) no. 1, pp. 19-37. doi : 10.4064/ap82-1-3. http://geodesic.mathdoc.fr/articles/10.4064/ap82-1-3/

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