Surplus sharing is a kind of a fair division problem where the goal is to share the financial benefits of cooperation (the "economic surplus") among the cooperating agents.
When they all cooperate in a joint venture, the total gain is u1+...+un+s, where s>0.
This s is called the surplus of cooperation, and the question is: what is a fair way to divide s among the n agents?
Chun[2] presents a characterization of the proportional rule.
Moulin[3] presents a characterization of the equal and proportional rule together by four axioms (in fact, any three of these axioms are sufficient): Any pair of these axioms characterizes a different family of rules, which can be viewed as a compromise between equal and proportional sharing.