<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We introduce, in the first part, the notion of weakly convex pair of correspondences, we give its economic interpretation, we state a fixed point and a selection theorem. Then, by using a tehnique based on a continuous selection, we prove existence theorems of quilibrium for an abstract economy. In the second part, we define the weakly biconvex correspondences, we prove a selection theorem and we also demonstrate the existence of equilibrium for a generalized quasi-game (2003 Kim's model). In the last part of the paper, we give other applications in the game theory, finding equilibrium for abstract economies having correspondences with weakly convex graph. We show that the equilibrium exists without continuity assumptions. </p></abstract>

We introduce, in the first part, the notion of weakly convex pair of correspondences, we give its economic interpretation, we state a fixed point and a selection theorem. Then, by using a tehnique based on a continuous selection, we prove existence theorems of quilibrium for an abstract economy. In the second part, we define the weakly biconvex correspondences, we prove a selection theorem and we also demonstrate the existence of equilibrium for a generalized quasi-game (2003 Kim's model). In the last part of the paper, we give other applications in the game theory, finding equilibrium for abstract economies having correspondences with weakly convex graph. We show that the equilibrium exists without continuity assumptions.

Equilibrium existence under generalized convexity

Department of Mathematics, University of Bucharest, 14 Academiei Street, 010014 Bucharest, Romania

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Equilibrium existence under generalized convexity"}

We introduce, in the first part, the notion of weakly convex pair of correspondences, we give its economic interpretation, we state a fixed point and a...

Equilibrium existence under generalized convexity

Published Online: May 21, 2013

Page range: 95 - 110

DOI: https://doi.org/10.2478/v10309-012-01058-8

Keywords
weakly convex pairs of correspondence, weakly biconvex correspondences, weakly convex graph, fixed point theorem, continuous selection, abstract economy, equilibrium

This content is open access.

Equilibrium existence under generalized convexity

Published Online: May 21, 2013

Page range: 95 - 110

DOI: https://doi.org/10.2478/v10309-012-01058-8

Keywordsweakly convex pairs of correspondence, weakly biconvex correspondences, weakly convex graph, fixed point theorem, continuous selection, abstract economy, equilibrium

This content is open access.

Keywords
weakly convex pairs of correspondence, weakly biconvex correspondences, weakly convex graph, fixed point theorem, continuous selection, abstract economy, equilibrium