The even split rule in positive assortative matching

Many economic models, especially in two-sided matching literature, involve breaking down a supermodular function into two supermodular functions according to a certain allocation rule. The conventional wisdom is to invoke the Nash bargaining solution, which boils down to an even split rule within the transferable utility framework. This paper rationalizes the use of the Nash bargaining solution in a two-sided matching model by showing that the even split rule is the only allocation which allows the net benefit functions to inherit supermodularity from the joint surplus function, which is necessary to ensure positive assortative matching.