On the Fair Allocations in the Two-sided Matching Problems

Abstract

Our purpose is to discuss the existence of fair allocations in two-sided matching problems. The existence of fair allocations is not guaranteed in general,however,it is a dense property in an appropriate topology. Several other topological properties are explored for the sets of problems with or without fair allocations. We give a necessary and sufficient condition for the existence of fair allocations in the separable utility case. The lattice structure and monotonicity property of the set of fair allocations are also examined.