On the Existence of Nash Equilibria in Asymmetric Sporting Contests with Managerial Efficiency

This paper considers a contest model of an n-team professional sports league. Teams can have different drawing potentials and different managerial skills to transform a given set of playing talents into playing performance. The analysis demonstrates that there exists a unique non-trivial Nash equilibrium under the general conditions (i.e., the revenue functions of the teams are concave, the production functions of the teams are strictly increasing and concave, etc). The proof uses the share function approach with the following two reasons: one is to avoid the proliferation of dimensions associated with the best response function approach and the other is to be able to analyze sporting contests involving many heterogeneous teams.