Yudkowsky has written about The Ultimatum Game. It has been referenced here 1 2 as well.
When somebody offers you a 7:5 split, instead of the 6:6 split that would be fair, you should accept their offer with slightly less than 6⁄7 probability. Their expected value from offering you 7:5, in this case, is 7 * slightly less than 6⁄7, or slightly less than 6.
While merely anti-bacterial, Nano Silver Fluoride looks promising. (Metallic silver applied to teeth once a year to prevent cavities).