Anonymity in sharing the revenues from broadcasting sports leagues

Abstract

We study the problem of sharing the revenues from broadcasting sports leagues axiomatically. Our key axiom is anonymity, the classical impartiality axiom. Other impartiality axioms already studied in broadcasting problems are equal treatment of equals, weak equal treatment of equals and symmetry. We study the relationship between all impartiality axioms. Besides we combine anonymity with other axioms that have been considered in the literature. Some combinations give rise to new characterizations of well-known rules. The family of generalized split rules is characterized with anonymity, additivity and null team. The concede-and-divide rule is characterized with anonymity, additivity and essential team. Other and combinations characterize new rules that had not been considered before. We provide three characterizations in which three axioms are the same (anonymity, additivity, and order preservation) and the fourth one is different (maximum aspirations, weak upper bound, and non-negativity). Depending on the fourth axiom we obtain three different families of rules. In all of them concede-and-divide plays a central role.