On the Importance of Uniform Sharing Rules for Efficient Matching

The paper aims to provide a possible explanation for the occurrence of uniform, fixed-proportion rules for sharing surplus in two-sided markets. We study a two-sided matching model with transferable utility where agents are characterized by privately known, multi-dimensional attributes that jointly determine the surplus of each potential partnership. We ask the following question: for what divisions of surplus within matched pairs is it possible to implement the efficient (surplus-maximizing) matching? Our main result shows that the only robust rules compatible with efficient matching are those that divide realized surplus in a fixed proportion, independently of the attributes of the pair's members: each agent must expect to get the same fixed percentage of surplus in every conceivable match. A more permissive result is obtained for one-dimensional attributes and supermodular surplus functions