Hmm.
Spoiler Below If there were one man wearing a red hat, learning that there was at least one man wearing a red hat would let him know that he had a red hat, and he could leave at the next strike of the clock.
If there were two men wearing red hats, upon learning that there was one or more men wearing red hats, both could know that they had red hats and leave on the second strike. They can each see at least one red hat, and they should have expected the owner of that hat to leave on the first strike if he was the sole wearer of a red hat.
If there were three men wearing red hats, all three should leave on the third strike. They can each see two red hats, and should have expected both owners of those red hats to leave on the second strike if they were the only wearers of red hats.
This can be extended to 15 people, who would all leave on the 15th strike having seen that the 14 people they each see with red hats have not figured out that they can leave yet.