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

Shumei Hirai

doi:10.5923/j.jgt.20120105.01

Abstract

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.

Highlights

This paper provides a general proof of the existence of pure-strategy Nash equilibria in an n-team sporting contest with heterogeneity of market size and of managerial efficiency among the teams
Since the seminal paper of[21], the Nash equilibriu m concept has been used in the analysis of professional team sports
This study has proven that under general conditions, a unique non-trivial Nash equilibriu mexists in a contest model of an nn-team sports league with different drawing potentials and different managerial skills among the teams

Summary

Introduction

This paper provides a general proof of the existence of pure-strategy Nash equilibria in an n-team sporting contest with heterogeneity of market size and of managerial efficiency among the teams. Ii So me emp irical studies, have found evidence that manageria l quality and e xperience is positively related to team and player performance ([10],[18]); in addit ion, some managers are more efficient than others at transforming a given set of player inputs into team wins ([14],[8]). These restrict ions most probab ly app ly to the Nash equilibriu m model in sports because of the difficulty in managing non-identical teams with respect to their market size and/or managerial efficiency by conventional means,.

The Model

Existence Analysis

Conclusions