Balanced sets appeared in the 1960s in cooperative game theory as a part of nonempty core conditions. In this paper we present a classification of balanced families containing only 2–element subsets. We also discuss generalizations of the classical Sperner and Tucker lemmas using balanced sets.
Bludov, Mikhail V., and Oleg R. Musin. "Balanced 2-subsets." arXiv preprint arXiv:2302.13453 (2023).