The women of Sevitan (from Herbert Gintis 1997)
The Sevitan live as monogamous families in a small village where virtually everyone knows what everyone else is doing, virtually all the time. The only information asymmetry is that no wife knows if her own husband is philandering, although every wife knows the behavior of every other husband in the village. The penalty for a philandering husband is to be branded by his wife with a purple P on the forehead in the middle of the night while sleeping. This penalty is only imposed by a wife who knows with certainty that her husband is guilty.
Needless to say, no husband is ever branded. But one day a woman from another village comes to visit. Upon leaving the next day, she confides in the women of Sevitan that there is at least one philanderer in the village. Nothing happens for five days. But on the sixth night a certain number of husband are branded with the purple P. How many husbands are branded? How many philandering husbands are there? How could this happen, since the departing woman didn’t tell the Sevitan women anything they didn’t know already - that there is at least onephilanderer in their midst?