Q: Every wife in the village instantly knows when a man...
If only one man is cheating, then every woman in the village knows that fact except for his wife. Since she knows at least one man is cheating and she doesn't know his name therefore the only man it could be is her husband. Stab.
If two husbands are cheating, every wife will know the name of one or two of them. The first night everyone is sure that some other husband will be killed. When none is (because the two cheated on wives already know one and only one name so don't kill their husbands), everyone will realize that not one but at least two husbands cheated. Those wives who only know of one husband who cheated realizes that their own husbands also cheated and kill them. Stab. Stab.
Extended, if X husbands cheat then they will be killed on day X, but not before because the victimized wives know of X-1 cheaters and will allow X-1 days to pass before they realize the number of cheaters exceed their known cheaters list.
yes, as I said... Hilarity ensues
I was thinking in that direction as well - but the wives must be able to *prove* that their husbands were unfaithful before the stab-fest commences. They only know about the indiscretions of other men, but can only kill their own husbands upon receiving proof.
What would probably happen is that each woman would write down a separate list of the cheating husbands, which would be handed in to the queen. She'd then collate the names and provide the proof of infidelity to the appropriate women. Stab, stab, stab. All on Day 1.