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

This paper 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 whereas mixed leagues in which small-market clubs are profit- and large-market clubs are win-maximizers (type-I mixed leagues) are dominated by all other leagues. In addition, we show that, 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 large-market clubs are profit- 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 members associations to profit-maximizing corporations. Moreover, it is socially desirable to reorganize large-market clubs first because, in mixed leagues, it is better if large-market clubs maximize profits instead of small-market clubs. Finally, we show that the invariance proposition does not hold in any league. In mixed (homogeneous) leagues, revenue sharing decreases (increases) social welfare. Given these results, homogeneous leagues should introduce revenue sharing; mixed leagues should not.