Monica Patriche: Equilibria for abstract economies in $B$-convexity, p.35-49

Abstract:

We study properties of correspondences and the existence of equilibria in the framework of $\mathbb{B}$-convexity, recently introduced by W. Briec and Ch. Horvath.We study correspondences with weakly $\mathbb{B}$-convex graph and prove that such a correspondence defined on a bimplex has a continuous selection. Finally we obtain results concerning existence of equilibria for economies with correspondences having weakly $\mathbb{B}$-convex graphs or having $\mathbb{B-}$WCGS-property and $\mathbb{B}$ e-WCGS-property.

Key Words: Fixed point, equilibria for abstract economy, $\mathbb{B}$-convexity, correspondence with weakly $\mathbb{B}$-convex graph, correspondence with $\mathbb{B-}$WCGS-property, correspondence with $\mathbb{% B}$ e-WCGS-property.

2000 Mathematics Subject Classification: Primary: 91B50,
Secondary: 91A06, 91A10, 91A44.

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