The following three definitions are all labeled "winner takes all." This erratum is relevant to some PSOC-related tutorials, animated population dynamics tutorial slides, and a tutorial appendix in the dissertation. Thanks to Qiucen Zhang for valuable conversations.

Nowak and May (1992):

In each round of our game . . . , each patch-owner plays the game with its immediate neighbours. The score for each player is the sum o fhte pay-offs in these encounters with neighbours. At the start of the next generation, each lattice site is occupied by the player with the highest score among the previous owner and the immediate neighbours. . . . The illustrations are for the case when the game is played with the eight neighbouring sites (the cells corresponding to the chess king's move), and with one's own site (which is reasonable if the players are thought of as organized groups occupying territory).

Winner-takes-all: A patch adopts the strategy of the one player that has the highest payoff among all the patch's neighbors and itself.
Self-interaction: Yes.

J. McKenzie Alexander

Winner-takes-all: Same as Nowak and May.
Self-interaction: No (by attempting to reproduce some of the blinkers reported in Alexander's tutorial at the Stanford website, it appears that the Alexander animations did not include self-interaction.

Liao (as described in the tutorial section of the 2010 dissertation)

Winner-takes-all: The payoffs of all the cooperators in a patch's vicinity (including itself) are pooled. The payoffs of all the defectors in a patch's vicinity are also pooled. The patch adopts the strategy corresponding to the highest pooled payoff. This is a propagule-like model that could represent, for example, the dispersal of seeds of plants.
Self-interaction: No.

The propagule-model tends to allow for a lot more survival of cooperators than the Nowak-and-May winner-take-all model. Survival of cooperators does not require high pay-off for each cooperator when they can combine their pay outs.