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I believe part of GP's point is that, for some sizes of village, there may not be any chance that your counterpart is a stranger. If your counterpart is not a stranger, even if you don't know their exact identity, you might choose to play more generously.

Anonymous, but still within a relatively small group.

There was also another party in the game whose identity was known well enough: word quickly spread of the young, square-jawed visitor from America giving away money

The Machiguenga had traditionally been horticulturalists who lived in single-family, thatch-roofed houses in small hamlets composed of clusters of extended families.

You're saying the family would never talk about this strange newcomer and his odd games and what he got me to do?