Social Welfare in Sports Leagues with Profit-Maximizing and/or Win-Maximizing Clubs

This article develops a contest model to compare social welfare in homogeneous leagues in which all clubs maximize identical objective functions with mixed leagues in which clubs maximize different objective functions. We show that homogeneous leagues in which all clubs are profit maximizers dominate all other leagues. Mixed leagues in which small-market clubs are profit maximizers and large-market clubs are win maximizers (type-I mixed leagues) are dominated by all other leagues. From a welfare perspective, large-market clubs win too often in (purely) win-maximizing and type-I mixed leagues; whereas, small-market clubs win too many games in (purely) profit-maximizing leagues and in mixed leagues in which largemarket clubs are profit maximizers and small-market clubs are win maximizers (type-II mixed leagues). These results have important policy implications: Social welfare will increase if clubs are reorganized from non-profit member associations to profit-maximizing corporations. Moreover, we show that revenue sharing decreases (increases) social welfare in mixed (homogeneous) leagues.