Oh, I think "punishment" is just fine as a word to describe the proper treatment of defectors, and it is actually used routinely in the game-theory literature for that purpose. However, I'm not so sure I would agree that the babies in the story are being "punished".

I would suggest that, as powerless agents not yet admitted to the coalition, they ought to be treated with indifference, perhaps to be destroyed like weeds, were no other issues involved. But there is something else involved - the babies are made into pariahs, something similar to a virgin sacrifice to the volcano god. Participation in the baby harvesting is transformed to a ritual social duty. Now that I think about it, it does seem more like voodoo than rational-agent game theory.

However, the game theory literature does contain examples where mutual self-punishment is required for an optimal solution, and a rule requiring requiring one to eat one's own babies does at least provide some incentive to minimize the number of excess babies produced.