On the Robustness of the Extension of the One‐Third Law of Evolution to the Multi‐Player Game

We show that the extension of the one‐third law of evolution from the 2‐player game to the d‐player game is the same for all exchangeable models in the domain of application of the Kingman coalescent in the limit of a large neutral population. The extension relies on an approximation of the probability of fixation of a single mutant in terms of expected times in ancestral sample states that are calculated by induction. An interpretation based on the concept of projected average excess in payoff is discussed.