The Ebbs and Flows of the Game: Multiple Equilibria in a Sports League Model

Abstract

The history of professional sports leagues is rich with examples of clubs that enjoy success on the field for a number of seasons, only to fall back in subsequent seasons. Although some clubs achieve consistent success, and a few, consistent failure, most clubs display a cyclical pattern as they ‘‘make a run’’ for success, then take fallback positions. This behavior is difficult to explain using the now standard league model of Fort and Quirk. In this article, the authors discuss the likelihood of this cyclical behavior emerging in the standard model and then develop an extension to the model, which can generate movements between good (team success) and bad (team failure) equilibria. The authors then discuss the stability conditions for each equilibrium and the conditions under which a club might find one of these equilibria unsustainable in the long run.