On the existence of maximal elements: An impossibility theorem

Abstract

Most properties of binary relations considered in the decision literature can be expressed as the impossibility of certain ``configurations.'' There exists no condition of this form which would hold for a binary relation on a subset of a finite-dimensional Euclidean space if and only if the relation admits a maximal element on every nonempty compact subset of its domain.Binary relation; Maximal element; Necessary and sufficient condition; Potential games