Journal of the
Korean Mathematical Society JKMS

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 prove existence theorems of equilibrium points in qualitative games with preference correspondences and in $n$-person games with constraint and preference correspondences for non-paracompact setting of commodity spaces.

Keywords: $G$-convex space, $\Gamma$-convex set, $G$-KKM, abstract economy, correspondence, $n$-person game, equilibrium, qualitative game, $\Gamma$-quasiconcave

MSC numbers: Primary 54H25, 90D06, 46N10