In a recent comment, Fort and Winfree claimed to clear up some confusion about the implications of contest theory and the game theoretic approach to modeling contests, following the earlier work of Szymanski and Kesenne. Among other things they claimed to show that the invariance principle can still survive in the game theoretic interpretation. This note shows that the approach they suggest was already fully and explicitly adopted in the works cited above and that the invariance principle cannot hold for any plausible contest success function.
FortR.WinfreeJ. (2009). Sports really are different: The contest success function and the supply of talent. Review of Industrial Organization, 34, 69–80.
2.
FortR.WinfreeJ. (2012). Nash conjectures and talent supply in sports league modeling: A comment on current modeling disagreements. Journal of Sports Economics, 13, 306–313.
3.
HirshleiferJ. (1989). Conflict and rent-seeking success functions: Ratio vs. difference models of relative success. Public Choice, 63, 101–112.
4.
MaddenP. (2010). Game theoretic analysis of basic team sports leagues. Journal of Sports Economics, 12, 407–431.
5.
SzymanskiS. (2003). The economic design of sporting contests. Journal of Economic Literature, 41, 1137–1187.
6.
SzymanskiS. (2004). Professional team sports are only a game: The Walrasian fixed-supply conjecture model, contest-Nash equilibrium, and the invariance principle. Journal of Sports Economics, 5, 111–126.
7.
SzymanskiS.KesenneS. (2004). Competitive balance and revenue sharing in team sports. Journal of Industrial Economics, 52, 165–177.
8.
TremblayV. (2009). Introduction: Economic issues in sports. Review of Industrial Organization, 34, 1–4.
