Abstract
In this paper, we deal with a general equilibrium problem where a bimap F: A×B ⊑ X×Y→2Z is involved. This problem contains the scalar equilibrium problem as a very special case. The general equilibrium is considered via the properties of the map G: B→2A naturally associated to the problem. The main result shows that, to have solutions on every convex subsets B1 of B, localized via a map T: B→2A, a necessary and sufficient condition is the KKM property of the map G with respect to T. The assumptions require that T satisfies a regularity condition with respect to G, and it is proved that this condition is quite sharp, providing a suitable counterexample.
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