Some Observations on Fort and Winfree “Nash Conjectures and Talent Supply in Sports League Modeling

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.