# COINCIDENCE THEOREMS ON A PRODUCT OF GENERALIZED CONVEX SPACES AND APPLICATIONS TO EQUILIBRIA

• Park, Se-Hie (Department of Mathematics Seoul National University) ;
• Kim, Hoon-Joo (Department of Computer Science Daebul University)
• Published : 1999.07.01
• 65 3

#### Abstract

In this paper, we give a Peleg type KKM theorem on G-convex spaces and using this, we obtain a coincidence theorem. First, these results are applied to a whole intersection property, a section property, and an analytic alternative for multimaps. Secondly, these are used to proved existence theorems of equilibrium points in qualitative games with preference correspondences and in n-person games with constraint and preference correspondences for non-paracompact wetting of commodity spaces.

#### Keywords

G-convex space;$\Gamma$-convex set;G-KKM;abstract economy;correspondence;n-person game;equilibrium;qualitative game;$\tau$-quasiconcave

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