Surplus Division and Effi cient Matching

We study a two-sided matching model with a finite number of agents and with transferable utility: agents on both sides of the market are privately informed about multi-dimensional attributes that determine the match value of each pair. Utility functions are assumed to be quasi-linear, and monetary transfers among agents are feasible. We ask the following question: what divisions of surplus among matched pairs are compatible with information revelation leading to an effi cient matching? Our main result shows that the only robust rules compatible with effi cient matching are those that divide the achieved surplus in a fixed proportion, independently of the attributes of the pair’s members. In other words, for effi cient matching it is necessary that all agents expect to get the same fixed proportion of surplus in every conceivable match. A more permissive result is obtained for one-dimensional attributes and supermodular value functions.