Envy-free division using mapping degree

Understand

In this paper we study envy-free division problems.

• The classical approach to such problems, used by David Gale, reduces to considering continuous maps of a simplex to itself and finding sufficient conditions for this map to hit the center of the simplex.
• The mere continuity of the map is not sufficient for reaching such a conclusion.
• Classically, one makes additional assumptions on the behavior of the map on the boundary of the simplex (for example, in the Knaster--Kuratowski--Mazurkiewicz and the Gale theorem).