Indirect Evolution and Aggregate-Taking Behavior in a Football League: Utility Maximization, Profit Maximization, and Success

Prinz Aloys

Abstract
An evolutionary model of European football was applied to analyze a two-stage indirectevolution game in which teams choose their utility function in the first stage, and their optimal talentinvestments in the second stage. Given the second-stage optimal aggregate-taking strategy (ATS)of talent investment, it was shown that teams may choose a mix of profit or win maximization astheir objective, where the former is of considerably higher relevance with linear weights for profits,and is more successful in the utility function. With linear weights for profit and win maximization,maximizing profits is the only evolutionarily stable strategy (ESS) of teams. The results changeif quadratic weights for profits and wins are employed. With increasing talent productivity, winmaximization dominates in the static and in the dynamic versions of the model. As a consequence, itis an open question whether the commercialization of football (and other sports) leagues will lead tomore profit or win maximization.

Keywords
indirect evolution; football leagues; utilitymaximization; profitmaximization; evolutionary; stability