Equal-sharing extra revenues from broadcasting sports leagues

We consider the problem of revenue-sharing from broadcasting sports leagues by focusing on the axiom of equal benefits from additional viewers introduced in Bergantiños and Moreno-Ternero (J Math Econ 90:65–73, 2020a). This axiom states that when only adding audience to a particular game, the involved teams and non-involved teams should be respectively affected by the same amount. We show that this axiom, order preservation, and non-negativity characterize the family of convex combinations of the uniform rule and the equal-split rule. Replacing non-negativity with maximum aspirations yields convex combinations of the equal-split rule and concede-and-divide, whereas replacing it with weak upper bound yields convex combinations of the uniform rule and concede-and-divide. Moreover, by separately considering the impacts on involved and non-involved teams, we decompose equal benefits from additional viewers into two axioms. We then show that replacing either of its decomposition axioms with reallocation proofness maintains the validity of the axiomatizations.